A quantitative treatment of micellar effects upon deprotonation

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J. Phys. Chem. 1980, 84, 2611-2618 (22) Boyd, R. H. I n “Solute-Solvent Interactions”; Coetzee, J. H.; Rkchie, C. D., Ed., IMarcell Dekker: New York, 1969; Chapter 3. (23) Stigter, D., Prog. Co//oMPolym. Sci. 1978, 65, 45, and references cited. (24) Although the model is qualitatively satisfactorythere are wide variations in the estimtted ion-exchan e parameters for micellar binding of OHrelative to other anions!.za26 (25) Bunton, C. A; Carrasco, N.; Huang, S. K.; Paik, C. H.; Romsted, L. S. J. Am. Chem. SOC. 1978, 100, 5420. (26) Quina, F. I-I.; Chaimovich, H. J. Phys. Chem. 1979, 8 3 , 1844,

(27) (28) (29) (30)

(31)

Chaimovlch, H.; Bonilha, J. 8. S.; Poliil, M. J.; Quina, F. H. IbM. 1979, 83, 1851. Mukerjee, P. Adv. ColioidInterface Sci. 1967, 7, 241. Fisher, L. F.; Oakenfull, 0. 0. 0.Rev. Chem. SOC. 1977, 6 , 25. Lindman, B.; Llndlbom, G.; Wennerstrom, H.; Gustavsson, H. I n ref 2, Vol. 1, p 195. Reiss-Husson, F., Luzzatl, V. J . Phys. Chem. 1964, 68, 3504. Buist, G. J.; Bunton, C. A,,; Robinson, L.; Sepulveda, L.; Stam, M. J. Am. Chem. SOC.1970, 9 2 , 4072. Ciccolello, R. F.; Nlcoli, D.; Romsted, L. S., unpublished results.

A Quantitative Treatment of Micellar Effects upon Deprotonation Equilibria Clifford A. Bunton,” Laurence S. Rornsted, and LUISSepulveda’ Department of Chemistry, Udversity of California, Santa Barbara, California 93 106 (Received: March 20, 1980)

The apparent base dissociation constants, KB, for deprotonation of benzimidazole in dilute NaOH go through minima with increasing concentration of cetyltrimethylammonium ion surfactants (CTAX, X = C1, Br, NO3) at concentrations above the critical micelle concentration (cmc). However, KB decreases smoothly if the concentration of surfactant counterions is maintained at 0.1 M. In both cases the micellar effect on KB follows the sequence CTACl > CTABr > CTAN03. These observationsare consistent with a pseudophase ion-exchange model in which the micelle binds OH- and both forms of the indicator, increasing deprotonation and decreasing KB,but at the same time the counterion of the surfactant displaces OH- from the micellar surface so that KB goes through a minimum with increasing [CTAX]. This model leads to a very simple quantitative treatment which fits the data for [CTAX] > 0.01 M. A similar pattern of behavior has been found for deprotonation of phenols and oximes in CTABr in the presence of borate buffer. Intrinsic basicity constants in the micellar pseudophase can be estimated which are larger than those in water by approximately one order of magnitude.

Indicator equilibria provided the first examples of micellar-induced effects upon chemical reactions in aqueous solution.2 Hartley showed, for example, that deprotonation of nonionic indicators was increased by cationic and decreased by anionic micelle^,^ and his original conclusions have been supported by recent ~ 0 i - k . ~ ~ ~ A successful interpretation must account for some additional observations. (i) Apparent acid dissociation constants, KA, go through maxima with increasing concentration of cationic surfactant.6 (ii) Added salts decrease micellar effect,s upon acid-base equilibria and the magnitude of the effect increases with decreasing hydrophilicity of added couniterion to the m i ~ e l l e . ~ ? ~ ’ * ~ Two models have been used to explain these observations. The first relates the change in apparent acid disKA,to surface potential effects on the sociation consti~ts, interfacial pH rmd tho stability of the charged form of the i n d i c a t ~ r . ~The *~l~ second, the pseudophase ion-exchange model, places eimphasis on the ability of a cationic micelle, for example, to bind OH-, and thus to promote deprotonation of a wleak acid at the micellar surface.1° Various workers have shown how either of these models can account qualitatively for micellar effects on acid-base equilibria and reaction rates, and it is difficult to develop quantitative treatments which distinguish between them.5J1 The aim of this work was to apply the pseudophase ion-exchange mlodel, originally developed for micellar effects upon reaction r a t e ~ , ~ J Oto- equilibria, ~~ and we have examined deprotonation of benzimidazole, phenols, and oximes in alkaline media. Our basic assumption is that there will be a competition between OH[-and other anions, 0022-3654/80/2084-2611$01 .OO/O

e.g., C1-, Br-, or NO3-, for the cationic micelles. Thus deprotonation of an indicator at a cationic micellar surface will depend upon the intrinsic basicity constant of the micellar bound indicator and the availability of OH- in the micellar pseudophase. Maxima in K A are explained in terms of two opposing effects. (i) Cationic micelles bind OH- and both forms of the indicator, concentrating them in the small volume of the micellar pseudophase, and therefore shifting the equilibrium in favor of deprotonation. (ii) Additional surfactant “dilutes” the reactants in the increasing volume of the micellar pseudophase. In addition counterions, added as a simple salt, reduce deprotonation by expelling OH- from the surface of the cationic micelle. The relative affinities of the counterions for the cationic micelle are expressed in terms of ion-exchange parameter~’~J~ based on a model which is formally identical with that developed for counterion binding to po1yelectrolytes.l6 Micellar effects upon deacylation by the benzimidazolide anion (1) played a key role in the development of an un-

a-)a) t H20

%

1

+

OH-

2

derstanding of micellar cata1ysis,l3and therefore we have examined deprotonation of benzimidazole (2). Because we are using an ion-exchangemodel it is convenient to analyze the micellar effects in terms of the apparent basicity constants, KB. We have also examined deprotonation of phenols and oximes in connection with studies of micellar-catalyzed 0 1980 American Chemlcal Society

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The Journal of Physical Chemistry, Vol. 84, No. 20, 1980

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X,nm Figure 1. Spectra of 2 X M benzimklazole and its anion: (1) lo-' M Tris, pH 8.3; (2) lo-* M Tris, pH 8.3, 0.1 M CTABr; (3) 2 M NaOH; (4) 1 M NaOH, 0.1 M CTABr.

dephosphorylation by phenoxide and oximate anions.17 These observations are treated quantitatively in terms of a very simple pseudophase ion-exchange model.

Experimental Section Materials. Cetyltrimethylammonium bromide (CTABr) and sodium lauryl sulfate (NaLS) were purified by standard meth0ds.l' Cetyltrimethylammonium chloride (CTAC1) was prepared by alkylating Me3N (25% aqueous solution in i-PrOH) with hexadecyl chloride. The product was recrystallized several times (EtOH-Et20). Cetyltrimethylammonium nitrate (CTAN03)was prepared from CTABr and AgN03 in EtOH followed by several recrystallizations (EtOH-EtzO). Anal. Calcd for C19H42N203: C, 65.8; H, 12.2; N, 8.1. Found: C, 65.7; H, 12.2; N, 8.0. The surfactants had no minima in plots of surface tension against log concentration. Our values of the critical micelle concentration, cmc, in the absence of added solutes were CTAN03, W3;CTAC1, 1.8 as follows: CTABr, 9 X X lod3M. These values agree with literature values,18 and we use them in our treatment of the data. Benzimidazole was decolorized (charcoal) and recrystallized (aqueou EtOH): mp 172 "C, lit.19mp 171 "C. The purification or preparation of the other indicators has been described.17 Inorganic electrolytes were generally used as the sodium salts, but we used both NaN03 and KNOB,and found their behaviors to be identical. Absorbance Measurements. Absorbances were measured at 25.0 "C with either a Gilford or a Beckman 5260 spectrophotometer with reference solutions of identical composition less the indicator. Deprotonation of Benzimidazole. Two values of pKA are quoted for the deprotonation of benzimidazole in water: 11.2620and ca. 12.3.21 Our value of 12.78 was measured spectrophotometrically at 282 nm, using 6 X M benzimidazole in NaOH. No correction was made for activity effects, Our experiments with benzimidazole were made using NaOH to avoid problems from micellar effects on buffer equilibria, and we estimated apparent classical basicity constants, KB,directly using eq 1, where BH and B- are KB = [B"l'I [OHT-l/ LBT-1 (1) respectively benzimidazole and its monoanion, and the subscript T denotes concentrations in terms of total solution volume. Figure 1shows the effect of CTABr on the absorption spectra of benzimidazolide anion at high pH. (Inde-

Bunton et al.

pendent experiments showed that benzimidazolide anion is essentially fully micellar bound in CTAX solutions of M.) Benzimidazole does not absorb at greater than 289 nm, and some apparent dissociation constants for deprotonation were measured at this wavelength. However, we obtained better results by working at 286 nm where there is a small contribution of absorbance by benzimidazole. This absorbance could be neglected except for surfactant concentrations close to the cmc, and we estimate the same valves of KB using either wavelength. In calculating KBwe allowed for depletion of OH- due to deprotonation of benzimidazole. The correction was generally very small for both and M benzimidazole. In calculating the concentration of benzimidazolide anion we used the following extinction coefficients: 6300 and 4170 at 286 and 289 nm, respectively. We found the same extinction coefficients, within experimental error, in 0.1 M CTABr + 1M NaOH, 0.01 M CTANOB+ 0.1 M NaOH; 0.05 M CTACl with 0.1 or 0.5 M NaOH. Changing [benzimidazole] from to M did not change the extinction coefficient. However, the extinction coefficient in 0.01 M CTANOBand 1 M NaOH was 4400 at 289 nm and this value was used for calculations in these solutions. Deprotonation of Phenols and Oximes. These indicators are generally too acidic to be used in solutions of NaOH. We used 0.01 M borate ion, because it appears to interact only weakly with cationic micelles. The apparent acid dissociation constants are given by eq 2, where [H+] KA [ROT-][H+1/[ROHTI

(2)

is assumed to be given by the pH of the solution measured in the presence of surfactant, i.e. pH = -log [H+]

(3)

The indicator concentrations were 2 X M for alkylphenols and acetophenone oxime and W4M for pnitrobenzaldoxime." Our values of pKA for deprotonation in water were taken from the literature22or, where necessary, were measured spectrophotometrically. The values of the base dissociation constant in water, pKBW,were calculated from pKAand pKw as follows: pKB = PKW

- pKA

(4)

In water pKw = 14, and we use this value in estimating the apparent base dissociation constants, KB, in the presence of micelles. Deprotonation of acetophenone oxime was followed in dilute NaOH with the pH adjusted to 11.37. Measurements were made at the following wavelengths: p-cresol, 297 nm; p-n-propylphenol, 296 nm; p-tert-butylphenol, 292 nm; p-tert-amylphenol, 293 nm; 2-naphthol, 343 nm; ptert-butoxyphenol, 307 nm; p-nitrobenzaldoxime, 357 nm; acetophenone oxime, 268 nm. One set of experiments was made by using 2 x M p-tert-butylphenol in 0.005 M CTABr with added NaBr. At this surfactant concentration both the phenol and phenoxide ion were fully micellar bound,23even at the highest [NaBr]. This conclusion was verified by spectrophotometric measurement of the total micellar bound solutes at the isosbestic point between phenol and phenoxide i0n.l' These experiments in dilute NaOH were carried out with exclusion of COB. Binding Constants. The binding constants, Ks, M-l, of the neutral indicators to micellized CTAX were determined spectrophotometricallyfollowing methods described e l s e ~ h e r e : ~ benzimidazole, ',~~~~~ 36 in CTABr and CTAN-

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Micellar Effects upon Deprotonation Equilibiria

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Flgure 2. Micellar effects upon the deprotonation of benzimidazole: (0, 0) CTACI; (11, 0)CTABr; (+, 0) CTAN03. Open points in the M benM NaOM and 1.8 X absence of salt, and with 2 X zimidazole; solid points 5 X I O 3 M NaOH and :2 X IO3 M benzimidazole and 0.1 M total anion concentration.

03, and 43 in CTAC1,50 in [CTACl] t [NaCl] = 0.1 M and 68 in CTACl + NaCl > 0.5 M; and in CTABr, p-nit,ro-

benzaldoxime 240, acetophenone ogime 150. Binding constants of the phenols and phenoxide ions have been published.23 Our values of K, for benzimidazole agree well with the literature value of 36 in CTABr.21 The corresponding binding constants, K;, M-l, of the anions in CTABr were benzimidazolide, 2400 (2 M NaOH); acetophenone oximate, 616 (0.1 M NaOH). The other values have been r e p ~ r t e d . ~ ‘ ~ ~ ~ ~

Results Micellar Effects upon Deprotonation. The variation of the apparent base dissociation constants of benzimidazole in surfactant solutions in NaOH is shown in Figure 2. The values of pKB go through maxima with increasing surfactant concentrations, i.e., KB goes through minima and K Athrough maxima, and the micellar effect follows the sequence CTACl > CTAI3r > CTAN03. The maxima disappear if the concentration of counterion is kept constant* The two sets of measurements of pKB in 0.1 M CTAX agree, although they were made at different times with different IOHT-] and [benzimidazole]. Deprotonation of phenols and p-nitrobenzaldoxime was followed in borate buffer, but again we found maxima in PKB (minima in KB) with increasing [CTABrIa6Examples of this behavior are shown in Figure 3, and additional data are in Table S1 (see paragraph at end of text regarding supplementary material). The variation in pKB depends upon the hydrophobicity of the indicator. For example, with the less hydrophobic indicators we see no effect in very dilute CTABr, ahowing that monomeric surfactant has little effect on KB. But with the more hydrophobic phenols pKB increases at very low [CTABr] because of induced micellization or interaction with submicellar aggregates. Treatment of Acid--Base Equilibria. The micellar effect upon deprotonation of the indicator, BH, is assumed to depend upon the distribution of OH- and the indicator species between the aqueous and micellar pseudophases and not directly upon the total amount of OH- in solution. We assume also that simple ion exchange (eq 5 ) governs the concentrations of [OHw-] (in the water) and [OHM-]

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Flgure 3. Micellar effects upon the deprotonation of phenols (+, A, M) and p-nitrobenzaidoxime (0)at pH IO, 0.01 M borate buffer.

(in the micelle). The quantities in brackets are molarities calculated in terms of the total solution volume. (5) KXoH = rOHW-1 [XM-] /[OHM-] LXW-1 X = C1, Br, NO3 Deprotonation of micellar bound BH is, however, assumed to depend on mOHswhere6Il2 mOHs= [OHM-]/ ([ CTAX] - cmc) (6) Le., it is the mole ratio of micellar bound OH- to micellized surfactant and a base dissociation constant in the micelle, KBM,is defined as KBM= mOHs[BHMl/ rBM-1 = [OHM-][BHM]/([CTAX]- C~C)[BM-] (7) The constant KBMis, dimensionless, and by using this form we evade the problem of defining the volume of micellar pseudophase in which reaction takes place>12 and the various equations take simple forms. In the ion-exchange model, the concentration of OH- in the micellar pseudophase depends critically on the quantity of counterion, X-, in the solution and the relative affinities of the two ions for the micelle surface, KxoH(eq 5 ) . We used several approximations in developing the model for deprotonation, which restrict its application to results in relatively high concentrations of surfactants (>0.01 M CTAX). However, these results are the more reliable because uncertainties in the concentration of monomeric surfactant and perturbation of the micelles by the solutes are minimized. Because the treatment is based on competition between hydroxide ion and the micellar counterion it is not strictly applicable to buffered solutions. Nevertheless, it appears to be satisfactory for deprotonations in borate buffer, but it could not be applied to carbonate, phosphate, or amine buffers. Provided that OHdoes not compete effectively with halide or nitrate ion (X-) for a site on the micellar surface, [&-I >> [OHM-]when [OH,] is small, so that [&-I = (1- a)([CTAX] - cmc) (8) [X,] = cmc + a([CTAX] - cmc) (9) where cy is the degree of counterion dissociation of the micelle.10v26This approximation appears to hold for Br-

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The Journal of Physical Chemistry, Vol. 84, No. 20, 1980

Bunton et al.

TABLE 1: Deprotonation of Benzimidazole in

[NaNO31,M

Surfactant-Salt Mixtures

surfactant

salt

K KPH M.

I O ~ K ~ V ,

M ~ ~ CTABra NaBr 0.05 0.25 2.4 (4.0) 1.7 (2.8) CTAN03a NaNO, 0.067 0.35 2.9 2.0 CTACP NaCl 0.0148 0.5g CTABrb NaBr 0.041 0.28 2 . 0 ( 3 . 3 ) 1.4 (2.3) CTABrC NaBr 0.053 2.5 (4.2) 1.8 (3.0) CTANO,d NaNO 0.064e 2.8 1.9 CTAN03d NaNO, 0.075f 3.3 2.3 a 0.1 M total anion, 2 X M OH'. 0.015 M NaBr, 2X M OH-. With added NaBr, see text. l o - *M CTANO,, variable [NaNO, e and M OH-. 0.1 M OH-. g See text. Calculated by using values of KXoH from ref 30; values in parentheses are based on KxoH from ref 15. ._

a

1

0-3

~

E

[CTAX], M

cmc, and the problem is compounded by induced micellization by the solutes or by interactions between the solutes and submicellar aggregate^.^^ We see no simple way of dealing with this but it can be significantly reduced by working at surfactant concentrations well above the cmc and in the presence of salts which reduce the cmc. Deprotonation of Benzimidazole. Experiments were done under a variety of conditions by using CTABr, CTAC1, and CTAN03 surfactants with and without added salts (Figure 2 and Tables S2 and 53). Experiments at Constant Counterion Concentration. Equation 13 takes a simpler form if the counterion concentration is kept constant and several experiments were done in solutions where [CTAX] + [NaX] = 0.1 M and X = C1, Br, NO3 (Figures 2 and 4). Under these conditions, and at relatively high surfactant concentration, we can neglect the contribution of the cmc, and eq 13 simplifies to

Figure 4. Treatment of the deprotonation of benzimidazole in saltsurfactant mixtures: (0)CTABr, 0.1 M Br-; (0) CTANO,, 0.1 M NO3and 2 X M OH-. Solid points 0.01 M CTANO, with added NaNO, in (A)0.001 M OH'; (+) 0.01 M OH-; ( 0 )0.1 M OH-.

and NO; counterions, but fails for the C1- counterion (see Discussion). In the absence of added salt and provided that CY' ([CTAX] - cmc) >> cmc, the base dissociation constant KBMis given by

The concentration of micellar bound BHM is given by lBHMI / [BHTI = K,([CTAX] - cmc)/[l + K,([CTAX] - crnc)) (11) but under our conditions B- is wholly micellar bound, i.e., [BM-! = [BT-] (see Experimental Section and ref 23). With these simplifications we obtain

KB = [OHw-l([BHwI + [BHMI)/[BM-] (12) and eq 10-12 give KB = KBMKxoH[a([CTAX]- cmc) -t cmc) X (1+ K,([CTAX] - cmc))/[K,(l - a)([CTAX] - crnc)] (13) Equation 13 has the appropriate form in that KB goes through minima, i.e., K Agoes through maxima, with increasing [CTAX]. However, a major problem with eq 13 is that KBMKXoH, calculated by use of this equation, depends critically upon CY.Unfortunately, the cited values of CY depend on the experimental method, and although most are in the range 0.1-0.3 for a wide range of surfactants,26bthis uncertainty complicates our analysis of the data (see Discussion). However, the problem is simplified markedly by the addition of salt containing the surfactant anion, and a number of experiments were carried out in the presence of added salt. In some experiments the concentration of counteranion was kept constant; in others salt was added to a constant concentration of surfactant. In the presence of excess counterion the concentration of anion in the aqueous pseudophase is not strongly dependent on the degree of dissociation, CY, of the micelle, and in favorable conditions we can estimate CY from our data. In addition, the added anion displaces OH- from the micelle, which reduces some of the uncertainties introduced by the assumptions made in the derivation of eq 13. An additional problem arises from the assumption that the cmc measures the amount of monomeric surfactant in solution.25This assumption is probably correct only at the

e

This equation has a convenient form because we can calculate 1 - a from the slope/intercept (Figure 4). The values of CY (Table I) for bromide and nitrate are at the upper end of the range of values generally reported,26but the value for chloride is much larger than expected, which is almost certainly due to a breakdown in the assumptions of our treatment. The values of CY = 0.25 and 0.35 for bromide and nitrate respectively are probably within the uncertainty of our method, in part because they depend upon an extrapolation to determine the intercept, but also because the approximations involved in eq 14 become more serious as the surfactant concentration is decreased. From the slopes of the plots (Figure 4) we obtain KBMKXoHfor CTABr and CTAN03(Table I). The values of these parameters follow the expected strengths of binding of the anions to the micelle, NO3-> Br-, in accord with other e v i d e n ~ e ~ Jand ~ J qualitatively ~*~~ it is evident that KBroH> KCIoH. Experiments with Varying Counterion Concentration. In one set of experiments we added NaBr to CTABr with the intention of maintaining [Br,] at 0.015 M (Table S2), on the assumption (which is probably erroneous) that, for CTABr, CY = 0.15, so that for CTABr up to 0.1 M: [NaBr] = 0.015 - a[CTABr] 115) and eq 13 takes the form KB = KBMKB,OH(O.015 + (1 - cu)cmc) X (1+ K,([CTABr] - cmc))/[(l - a)K,([CTABr] - cmc)] (16)

Micellar Effects upon Deprotonation Equilibria

The Journal of Physical Chemistry, Vol. 84, No. 20, 1980 2615

TABLE 11: Dleprotonation of Phenok and Oximes in CTABr*

p-cresol 485 2.5 25 1.2 ( 2 . 0 ) 8 (14) p-n-propylphenol 1350 2.6 26 1.2 (2.0) 8 (14) 33 1.6 ( 2 . 7 ) 11 (19) 1700 3.3 p-tert-butylphenol p -tert-amylphenol 4330 2.7 27 1.3 (2.2) 9 (15) 1390 0.5 17 0.24 (0.4) 2-naphtho1 2 (3) p-tert-butyoxyphenol 1630 4.6 39 2.2 (3.7) 16 (26) p-nitrobenzaldoxime 240 1.6 23 0.8 (1.4) 6 (10) 150 2.3 12 11 ( 1 8 ) 77 (130) acet,ophenoneoxime a In 0.01 M borate buffer, pH 10, except for acetophenone oxime which was in OH-, pH 11.37. The values of K , for the M for the alkyl phenols, Calculated by taking K B =~ phenols are from ref 23. Calculated from eq 13, a! = 0.25. M for p-tert-butyoxyphenol, 3 X M for 2-naphthol, 7 X M for p-nitrobenzaldoxime, and 2 X M for 1.2 X acetophenoneoxime. Calculated for KB,O~= 21, the values in parentheses are for K B , O ~= 12.5.

Equation 16 predicts that KBKB([CTABr]- cmc)/(l + K,([CTABr] -- cmc)) should be constant, as is found, and if a = 0.25 and cmc = 9 X M,KBMKXoH= 0.053 in good agreement with results in 0.1 M NaBr + CTABr (Table I). In another set of experiments in C'rABr we added 0.015 M NaBr to thle solution (Table S2),i3nd then eq 13 takes the form

qualitatively that the salt order for KXoHis NO3- > Br> C1-. Equation 13 can be rearranged to give K&,([CTAX] - cmc) K B ~ K x ~ ~ [CTAX] + l-ff 1 + ([CTAX] - cmc) KgMKpcmc (19)

The experiments in CTABr and CTACl fitted eq 19 and the respective slopes were 6 X and 4 X but for KBK,([CTA13r] - cmc) experiments on CTAN03 a linear plot was obtained only ----KBMKB,"H[CTABr] for [CTAN03] > 0.04M where the slope was If a = l-ff 1 K,([CTABr] - cmc) 0.25 and 0.35 for CTABr and CTAN03, respectively, we K B ~ K B ~ ~ [ C T A B ~ ] 0.015 cmc(1 - ( Y ) K B ~ K B ~ ~ x respectively for the estimate 0.06 and 0.07for KBMKXoH l-ff l-ff two surfactants in reasonable agreement with results in 0 . 0 1 5 K ~ ~ K ~ ~ the ~ ~presence of added salts (Table I). (17) As with many types of experiments in micellar solutions, 1- a the results in the presence of added salts are more reliable because 0.015>> (1-- a)cmc. The cmc of CTABr in water and easier to interpret than those in pure surfactant. In (9 X M) is decreased by added salt.18 The data in our experiments, the values of our constants are inde[CTABr] I0,02M fit eq 17,and from the slope and inpendent of a, or depend only on 1 - a (eq 14,16,17,and respectively, we estimate tercept of 0.0 16 and 8.4 X 18) (which is close to unity) in the presence of added salts. a = 0.28. Whien this value and that of the slope is used, In pure surfactants, a / ( l - a) (eq 13)is very sensitive to KB'KXoH is 0.041,in reasonable agreement with the values the value of a. However, there is the problem that added from other experiments in CTABr (Table I). salts affect micellar properties and may change the value For experiments with added NO3- we kept CTAN03at of a and the equilibrium constants in eq 13. 0.01 M and aldded NaN03 (Table 53). Deprotonation of Benzimidazole i n CTANO, + N a N 0 3 At this surfactant concentration the contribution of the Berezin and his co-workers observed that addition of nicmc can be neglected and eq 13 simlplifies to trate ion decreased the extent of overall deprotonation of micellar bound benzimidazole, and they postulated that KBK, [CTANO31 benzimidazolide ion was being expelled from the cationic 1 + KB[CTAN03] micelle by NO,5 X M. (As noted earlier we cannot apply our Experiments without Added Counterions. Values of KB approximate treatment to data at low [CTABr].) The were measured in CTAC1, CTABr, and CTAN03 with 5 values of KBMKBroHcalculated with a = 0.25 are in Table X loW3 M NaOH. Figure 2 illustrates the results for the 11. They do not depend upon the hydrophobicity of the effect of increasing surfactant concentration on pKg in 5 phenol, but they are clearly related to KBw, the base disX M OH-, and, as noted earlier, these results show sociation constant in water.

+

+

+

+

-

The Journal of Physical Chemistry, Vol. 84, No. 20, 1980

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TABLE 111: Effect of NaBr upon pK, of Bound p-tert-Butylphenola

**O

3.96 1.96 3.90 3.85 3.87 5.66 3.84 7.41 3.83 10.7 3.81 13.8 16.7 3.80 23.1 28.6 3.79 a Measured by using 2 X M phenol NaOH, with ~ K =B14 - ~ K A . 5 X

CTABrb 4.70 4.66 4.56 4.26 4.06 3.94 3.82 3.74 3.68 3.60 and 3 X M M CTABr.

TABLE IV : Deprotonation of p-tert-Butylphenol in Micellized Sodium Lauryl Sulfate 103 x [NaLS],M

103 x [NaLS],M

PKB

~ K B

3.90 15 1 3.89 20 3 3.74 30 5 3.61 50 10 3.34 a With 2 x 10-4M p-tert-butylphenol in buffer, pH 10, and taking ~ K =B14 - ~ K A

3.19 3.09 2.94 2.79 .

M borate

Effect of Added Bromide Ion on the Deprotonation of p-tert-Butylphenol: This system is simple because the experiments were in 0.005 M CTABr with added Br(Table 111). The binding constants of the phenol and phenoxide ion are such that both forms of the indicator are fully micellar bound (Experimental Section and ref 23). In CTABr the directly measured value of K Ais greater than that in water (Table 111),but it decreases on addition of NaBr and eventually becomes smaller than that in water with NaBr, showing that Br- is not displacing the phenol or phenoxide ion from the micelle, but is instead displacing OH-, as is found for experiments with benzimidazole. Provided that the cmc is small relative to added [Br-1, eq 18 becomes

KB =

K B ~ K B : ~ [ N ~ B ~K] B ~ K B , ' ~ [ C T A B ~ ] (20) 1-a 1-a

+

As predicted by eq 20 KB varies linearly with [NaBr] and - a) = 0.0085. If a = 0.25, the slope gives KBMKB,OH/(l as estimated from the experiments on benzimidazole (Table I), KBMKBroH = 0.0064. In principle, eq 20 allows us to calculate a from the slope/intercept, but the intercept is so close to zero that its value is only approximate. The which corresponds to a = 0.2. intercept is ca. Effect of Anionic Micelles. As expected anionic micelles of sodium lauryl sulfate (NaLS) decrease deprotonation of p-tert-butylphenol (Table IV). If one assumes that incorporation of the phenol into the anionic micelles protects it from deprotonation, Le., that the phenoxide ion does not bind and that anionic micelles do not incorporate components of the buffer, the simple distribution model leads to (KB/KBw) - 1 = K,([NaLS]

-

cmc)

al.

filtration, suggesting that the assumptions in the derivation of eq 21 are satisfactory.

PKB 103[NaBr], M

Bunton et

(21)

The hydrophobic phenol could reduce the cmc, but a plot of (KB/KBw) - 1 against [NaLS] is linear with an intercept of ca. M. The value of K, is 280 M-l calculated by using eq 21 and 320 M-' measured by ultra-

Discussion Significance of a. Micellar effects on deprotonation of the various indicators give values of the term KBMKXoH which are relatively insensitive to the medium or to changes in the hydrophobicity of a given type of indicator (Tables I and 11), and for benzimidazole they can be related to the expected sequence of KXoH,i.e., X = NO, > Br > C1.7J0J5130However, as noted earlier the approximations in our simple treatment are unsatisfactory for experiments in CTAC1, so that these data are only qualitatively significant. (A more complete treatment will be described elsewhere.) The use of a in eq 13 implies that, in our system, hydroxide and the counterion and the indicator are distributed uniformly throughout the micellar Stern layer and that a,and the acid-base equilibria in the micellar pseudophase, are not affected directly by ions in the aqueous pseudophase. This conclusion is consistent with conclusions on the distribution of counterions between aqueous and micellar pseudo phase^.^^ In kinetic systems there is evidence that the distribution of hydroxide ions about a cationic micelle may not fit the predictions of the simple Stern layer model when OH- is the only c o u n t e r i ~ nbut ,~~ there is good evidence that the Stern layer model holds when the more hydrophobic counterions Br- and NO,- are present.1°J5 Salt effects on the properties of polyelectrolytes also usually follow simple additivity rules rather than showing changes in counterion distribution as a function of salt concentration."j The values of KBMKXoH, estimated from experiments in the absence of salt, are very sensitive to a. For example, if a = 0.25 there are differences in the values of KBMKB:H determined from deprotonation of phenols in CTABr and borate buffer (Table 11),which are ca. 3 X and that estimated from the effect of Br- on the deof 6 X protonation of p-tert-butylphenol, eq 20 (Table 111). The two sets of data agree if a = 0.15, but this value of a differs from that estimated from the deprotonation of benzimidazole (Table I). The discrepancy may be more apparent than real because we are comparing results in borate buffer with those in hydroxide ion solutions, and the comparison may do no more than illustrate the sensitivity of the model to the value of (Y and the probability that it may not be constant. For example, there is extensive evidence that a! values are in the range 0.1-0.35 and are insensitive to the nature of the counterion or its concentration, but the same experimental methods give different results in the hands of different workers.26bConsidering the approximations in the treatments our values of a, derived from deprotonation of benzimidazole, are consistent with those in the literature, for example, a does not seem to be very sensitive to the nature of the counterion, and OUT estimates of a: for Br- and NO3- are consistent with other observations. The values of KBMKBrOH for the deprotonation of phenols depend very critically upon a. The use of a in these calculations implies a uniform Stern layer whose thickness is approximately equal to the diameter of the hydrated head However, a recent discussion of water penetration into the micelle suggests that the nature of the Stern layer could be very sensitive to added solutes, e.g., electrolytes,2eaand parameters such as KBMK~,OH/K~W (Table 11) vary slightly with the chemical nature of the indicator, although not with its hydrophobicity. In view of these assumptions and uncertainties regarding the nature of the reaction site at the water-micelle in-

Micellar Effects upon Deprotonation Equilibria

terface, only qualitative agreement between different types of experiments can be expected. Micellar rate enhancements present a similar situation, because second-order rate constants of bimolecular reactions in micelles are often similar to those in water, but only within one order of m a g n i t ~ d e . ~ J ~ - ' ~ J ~ ~ ' * Other Approximations in the Model. Calculation of an intrinsic basicity constant, KBM,from the treatment of the deprotonation of benzimidazole, phenols, and oximes requires knowledge of the ion-exchange constant, KxoH (see below). However, even without separation of these constants the data suggest that the controlling factor in micellar effects am deprotonation is the amount of basic ion in the micellar pseudophase, which if5 controlled by competition with the other anions. For example, if a counterion, e.g., Br-, were controlling deprotonation by competing with the indicator anion, e.g., the benzimidazolide, aryloxide, or oximate anion, for a site at the micelle surface, cf. ref 13, then the term KBMKxoHwould be very sensitive to the nature, and especially the hydrophobicity, of the indicator (Table 11). This conclusion is not affected by questions regarding either the applicability of the ion-exchange model to experiments with the phenols in borate buffer or the value of a. Another source of uncertainty stems from our method of calculating KB. For most of the experiments with benzimidazole we calculate KB directly from the stoichiometric concentrations of OH-, assuming that only a small amount of it is taken up by the micelle. But the experiments with phenols and oximes were run at a constant pH as measured by use of a glass electrode, so that we calculated KA,and thence KB, using eq 4, and taking pK, = 14, i.e., rssuming that the surfactant does not affect the autoprotolysis constant of water. This assumption may introduce absolute errors in KBMKxoH, but, again, it should not affect the relative values for a sieries of indicators. Role of Buffers in Acid Dissociation in Micellar Solutions. Although our evidence is limited, it seems that cationic micelles of CTABr do not interact strongly with borate ion, because the model appears to fit deprotonation of phenols in borate buffer. This result suggests that competition between Br- and OH- is of controlling importance even in borate buffer. However, our simple model fails for deprotonation of acetophenone oxime in phosphate buffer and of benzimidazole in dimethylamine or carbonate buffer, suggesting that these buffers are incorporated into cationic micelles (cf. ref 33). Dimethylmine would appear to be too hydrophilic to be incorporated into micellized CTABr, but thLere is evidence for micellar incorporation of ethanol.% We believe that the use of buffers complicates micellar effects upon acid-base equilibria and that caution should be exercised in interpreting the experimental results. Basicity Constants in the Micellar Pseudophase. Our treatment allows estimation of K B Mplrovided that KXoH (and a ) are known. Competition experiments on the binding of areinesulfonate ions to CTA+ micelles gives KxoH = 4.1,21, and 23 for X = C1, Br, and NO3,respect i ~ e l y . ~Another ~ estimation gives KCloH = 7.1 in C14H2,NMe3C1 and KBroH= 12.5 in CTABr, based on kinetic At the present time WE! have no reason to believe that one value is better than another. The values of KBM in Tables I and I1 are calculated by taking KBroH and KNO,'~ as 21 and 23, r e s p e ~ t i v e l y .The ~ ~ values in parentheses are based on KBrOH = 12.5.16 In aqueous NaOH we estimated K Bfor~benzimidazole as 6 X M (Experimental Section), and a reported value in buffer solution is 2 X 11D-' M." The values of KBwfor the phenols

The Journal of Physical Chemistty, Vol. 84, No. 20, 1980 2617

and oximes are given as footnotes in Table 11. The basicity constants, KBM,are calculated in terms of the mole ratio of micellar bound OH- to micellized surfactant head groups and are dimensionless. Conventional classical basicity constants in water, KBw, M, are calculated by using the molarity of hydroxide ion, but the two sets of constants can be compared provided that we estimate the molarity of OH- in the micellar pseudophase, using either the total volume of the micelle13 or an estimated volume of the Stern layer.6-28It is probable that deprotonation takes place in the Stern layer, and therefore we use its volume in calculating the molarity of OH- in terms of 1 L of Stern layer. On the assumption that the Stern layer extends to the a-methylene group of the surfactant, the volume of 1 mol of Stern layer has been estimated to be 0.14 L, Le., the molarity of OH- in the Stern layer is n0$/?.14.~ On this assumption, the basicity constant in the micellar phase, KBv,calculated in terms of the volume of the Stern layer is given by36 KBv = KBM/0.14 (22) The values of KBv are in Tables I and 11. For deprotonation of benzimidazole, where K B is measured directly, they are very similar to KBw in water, but for the phenols and oximes they are larger by approximately one order of magnitude. This difference may reflect our estimation of pKB from PKA,or our use of borate buffer in the experiments with phenols and oximes. Comparison of basicity constants in different media is fraught with uncertainty and our main conclusion is that micellar effects upon acid-base equilibria can be interpreted in terms of the pseudophase ion-exchange model originally applied to bimolecular ionic reactions, and that the dissociation constants so obtained are similar in magnitude to those in water. The surface of an ionic micelle appears to be highly a q u e o ~ s ,but ~ ~medium ~*~~ effects upon acid-base equilibria are important, so classical dissociation constants at the micelle surface would be expected to differ from those in water, For example, the polarities and dielectric constants of micelle-water interfaces appear to be lower than those of water,38and pK, has been estimated as 15.65 at the micellar surface.6 A key point of our work is that the differences in KB are not large and are not markedly dependent upon the nature of added solutes or the indicators. In addition, we see no reason to assume that ions in the aqueous pseudophase directly affect equilibrium constants, as expressed in eq 7, by changing the surface potentiad of the micelle. It is sufficient to assume that the added counteranions act by excluding the basic anion, e.g., OH-, from the micellar surface. This is not to say that Coulombic interactions between micellar head groups and counterions are unimportant, because it is these interactions which control the distribution of counterions between the aqueous and micellar' pseudophases. For example, salt effects upon indicator equilibria have been interpreted in terms of changes in surface potential: but the effects on KA are ion specific, so that any model, e.g., the Gouy-Chapman model, which treats ions as point charges must be unrealistic. At the present time it seems to us to be more realistic to describe the micellar binding of counterions in terms of the simple ion-exchange constants which are successfully applied to ion binding to ion-exchange resins and polyelectrolytes16and to cationic monomolecular layers.3g The ion-exchange constants can be measured directly whereas, except for monomolecular layers, surface potentials must h if&rred. The experiments on the monolayers were especially informative. In this system the specific interactions between

2018

The Journal of Physical Chemistry, Vol. 84,No. 20, 1980

the monolayer and a variety of counterions were accounted for in terms of an ion-exchange model, and changes in the measured surface potential were related directly to the selectivities of the monolayer toward different anions.39 Kinetic Implications. The analysis of rate-surfactant profiles for bimolecular reactions requires estimation of the concentrations of both reactants in the micellar pseudophase. The problem is especially acute for reactions of nucleophilic anions such as oximate, benzimidazolide, and phenoxide. In some systems the concentrations of the anions have been measured directly,14J7but in others they have been estimated indirectly from the variation of the apparent acid dissociation constants, KA, with surfactant concentration by using eq 23,13where K; is the binding KA = K A ~+ (K;([CTAX] ~ - cmc))/(l + K,([CTAX] - cmc)) (23) constant of nucleophilic anion, defined following eq 11. The decrease of KA at high [CTABr] and on addition of salt, e.g., KN03,was interpreted as a decrease in K; due to expulsion of the nucleophilic anion, e.g., benzimidazolide ion, from the micelle by counterions such as Br- or Our evidence suggests that this interpretation is incorrect and that estimates of second-order rate constants in the micellar pseudophase may therefore be in error. Some of the rate constants estimated by this method are at least one order of magnitude greater than those in water.13 Rate constants calculated by using directly measured concentrations of the anionic nucleophiles in the micelles are typically very similar to, or slightly smaller than, those in ~ a t e r , ~and J ~ we J ~believe that these results are the more reliable. Acknowledgment. Support of this work by the National Science Foundation (Chemical Dynamics Program) and the Army Research Office is gratefully acknowledged. Supplementary Material Available: Table S1, effects of CTABr on pKB of phenols and acetophenone oxime, Table S2, deprotonation of benzimidazole in mixtures of CTABr and NaBr, and Table S3, effect of hydroxide ion on deprotonation of benzimidazole in CTAN03+ NaN03 (3 pages). Ordering information is given on any current masthead page. References and Notes (1) Faculty of Sciences, University of Chile, Santiago, Chile. (2) Fendler, J. H.; Fendler, E. J. “Catalysis in Micellar and Macromolecular Systems”; Academic Press: New York, 1975; Chapter 6. (3) (a) Hartiey, G. S. Trans. Faraday SOC.1934, 30, 444. (b) “Micellization, Solubilization and Microemulsions”; MMal, K. L., Ed.; Plenum Press: Vol. 1, p 23. (4) Fernandez, M. S.; Fromherz, P. J . fhys. Chem. 1977, 87, 1755. (5) Funasaki, N. J . Phys. Chem. 1979, 83, 1999.

Bunton et al. (6) Bunton, C. A. Catal. Rev. Sci. f n g . 1979, 20, 1. (7) Bunton, C. A. I n “Reaction Kinetics in Micelles”; Cordes, E. H., Ed.; Plenum Press: New York, 1973; p 73. (8) Mukerjee, P.; Banerjee, K. J . Phys. Chem. 1984, 68, 3567. (9) Berezln, I. V.; Martinek, K.; Yatslmirskl, A. K. Russ. Chem. Rev. 1973, 42, 787. (10) Romsted, L. S. I n ref 3b, Vol. 2, p 509. (11) Almgren, M.; Rydhoim, R. J. Phys. Chem. 1979, 83,360. (12) Bunton, C. A. I n “Solution Chemistry of Surfactants”; Mlttal, K. L., Ed.; Plenum Press: New York, 1979; Vol. 2, p 519. (13) Martinek, K.; Yatsimlrski, A. K.; Levashov, A. V.; Berezin, 1. V. I n ref 3b. D 489. (14) Cuccovia, I.M.; Schroter, E. H.; Montelro, P. M.; Chaimovich, H. J. Org. Chem. 1978, 43,2248. (15) Quina, F. H.; Chaimovich, H. J . fhvs. Chem. 1979, 83, 1844. Chaimovich, H.; Boniiha, J. 8. S.; Poliil; M. J.; Quina, F. H. IbM. 1979, 83,1851. (16) Anderson, C. F.; Record, Jr., M. T.; Hart, P. A. Blophys. Chem. 1978, 7 , 301. Manning, G. S. Acc. Chem. Res. 1979, 72,443. (17) Bunton, C. A.; Cerichelli, G.; Ihara, Y.; Sepulveda, L. J . Am. Chem. SOC.1979, 107, 2429. Bunton, C. A.; Sepulveda, L. Isr. J. Chem. 1979, 81, 298. (18) Mukerjee, P.; Mysels, K. J. ”Critical Micelle Concentratlons of Aqueous Surfactant Systems”; NationalBureau of Standards: US. Government Printlng Office, Washington, D.C., 1970. (19) “Handbook of Chemistry and Physics”; Weast, R. C., Ed., 52nd ed.; Chemical Rubber Company: Cleveland, 1971. (20) Hisano, T.; Ichlkawa, M. Chem. Pharm. Bull. 1974, 22, 1974. (21) Yatsimirskl, A. K.; Oslpov, A. P.; Martinek, K.; Berezin, I. V. Koll. Z(€ng.) 1975, 37,470. (22) Fickling, M. M.; Fischer, A.; Mann, B. R.; Packer, J.; Vaughan, J. J . Am. Chem. Soc. 1959, 87,4426. Raouk, A.; Vilkas, M. Bull. Soc. Chim. Fr. 1988, 3315. (23) Bunton, C. A.; Se ulveda, L. J . fhys. Chem. 1979, 83, 680. (24) K, = [BHM]/[BH,r([CTAX] - cmc) where the subscrlpts M and W denote the mlceliar and aqueous pseudophases, respectively. (25) Menger, F. M.; Portnoy, C. E. J. Am. Chem. SOC.1987, 89, 4968. (26) (a) Menger, F. M. Acc. Chem. Res. 1979, 72,111. (b) For a survey of (Y values see, Romsted, L. S., Thesis, Indiana University, Bloomington, Ind., 1975. (27) Shiffman, R.; Rav-Acha, Ch.; Chevion, M.; Katzhendler, J.; Sarel, S. J. Org. Chem. 1977, 42,3279. Lindman, B.; Lindblom, G.; Wennerstrom, H.; Gustavson, H. In ref 3a, p 195. Atlk, S. S.; Singer, L. A. J. Am. Chem. SOC. 1979, 101, 6759. Farlnato, R. S.; Rowell, R. L. I n ref 12, Vol. 1, p 311, and references cited. (28) Bunton, C. A.; Carrasco, N.; Huang, S. K.; Paik, C.; Romsted, L. S. J. Am. Chem. SOC. 1978, 100, 5420. Bunton, C. A.; Romsted, L. S.; Smith, H. J. J . Org. Chem. 1978, 43,4299. (29) This sequence agrees with that estimated fr?m displacement of arenesulfonate ions from a cationic mlcelie. (30) Bartet, E.; Gamboa, C.; Sepulveda, L. J . fhys. Chem. 1980, 84, 272. (31) Stigter, D. Prog. ColloM folym. Sci. 1978, 65, 45. (32) Bunton, C. A.; Romsted, L. S.; Saveili, G. J. Am. Chem. SOC.1979, 707, 1253. (33) Funasaki, N. J. Phys. Chem. 1979, 83, 237. (34) Menger, F. M.; Jerkunlca, J. M. J. Am. Chem. SOC.1978, 100, 688. (35) Almgren and Rydholm estimate Khm = 40 from analysis of the rate-surfactant proflle for saponification of p-nitrophenyl acetate in solutions of CTABr.” This value is much larger than others cited. (36) I f KBVis calculated in terms of the total volume of the micelle its value is approximately halved so that ow conciusbns are not especially dependent upon our estimation of the volume of Stern layer. (37) Cordes, E. H. Pure Appl. Chem. 1978, 50, 617. (38) Cordes, E. H.; Gitier, C. Prog. Bioorg. Chem. 1973, 2, 1. Mukerjee, P.; Cardinal, J. R.; Desal, N. R. I n ref 3b, Vol. 1, p 241. (39) Plalsance, M.; Ter-Mlnassian-Sara@, L. J. c o l l o i d I n t ~ c eScl. 1978, 56, 33.