A Quantitative Treatment of Micellar Effects in Moderately

predicted by pseudophase ion-exchange treatments with constant fractional micellar ionization, u. A treatment based on solution of the Poisson-Boltzma...
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2130

Langmuir 1992,8, 2130-2134

A Quantitative Treatment of Micellar Effects in Moderately Concentrated Hydroxide Ion Clifford A. Bunton’ and John R. Moffatt Department of Chemistry, University of California, Santa Barbara, California 93106 Received February 18,1992. In Final Form: May 4, 1992

Cationic micelles increase first-order rate constants of reactions of OH-with p-nitrophenyl diphenyl phosphate @NPDPP),2,4dinitmhloronaphthalene(DNCN),and l,l,l-trichloro-2,2-bis@-chlorophenyl)ethane (DDT). T h e micellar rate e f f d with moderately concentrated OH- ()[X-,I 1+ 6 exp(-f/(l -f>)[X-,l

(3)

In eq 3, [X-,] is the concentration of X-in moles per liter of the aqueouspseudophase and 6 is a specificityparameter related to the (non-Coulombic)affinity of X- for the micellized cationic surfactant. Values of 6 will be low for hydrophilic, high charge density ions whose interactions with the micelle are largely Coulombic, and will be larger for polarizable, low charge density ions.12 We take 6 = 0 for the very hydrophilic ion OH-, and as in earlier work, we take 6 = 15 and 120 M-' for C1- and Br-, respectively.12 We assume that reaction occurs in a shell of thickness, A, at the micellar surface,and the first-order rate constant for the overall reaction is given by k, =

k,[OH,l

+ Iz,~K,([(CTA)XI - cmc)[OH-]

+

1 K,([(CTA)X] - cmc)

(4)

where k , and kzmare second-order rate constants in water and in the shell, K , is the substrate binding constant, [OH-IAis the average molarity in the shell, cmc is the critical micelle concentration in kinetic conditions,and X = C1 or Br. In the original treatment the micellar surface was assumed to be smooth and uniform, and we fitted the rate data on the assumption that N increases modestly with increasing [OH-], e.g., for (CTA)Br from N = 90 in 0.01 M OH-to 125in 0.05 M OH-.lPbscThe increase was smaller for (CTA)Cl. The fits deteriorated significantly with [OH-] > 0.1 M, although they were better than those given by the PIE in its classicalform,but predicted rate constanta were too low in 0.5 M OH-, with a constant k2m, even if we assumed a significant increase in N. (22) Aniansson, G. E. A. J. Phys. Chem. 1978,82, 2805.

2132 Langmuir, Vol. 8, No. 9, 1992

I

Bunton and Moffatt

mice1 le- water interface r = a

cell wall r=R

i

I

0.8

-6u-

k=

1 .o

I

Figure 1. An illustrationof the radial distributionof head groups about a mean position at the interface. I

f

8

.

0.41

.O-

e

o

1

I

r

0.6.B.

I

0.005

I

I

0.01

0.015

[CTABr],

z

I

0.02

M

Figure 3. Reaction of pNPDPP with 0.05 and 0.6 M OH-, 0 and 0, respectively, in (CTAIBr. The lines are predicted (Table I).

0.4-

Table I. Fitting Parameters for Nucleophilic Substitutions. substrate [OH-], M surfactant N 102kz=,M-18-1 DNCNb 0.03 (CTA)Cl 75 0.0115 DNCN 0.5 (CTA)Cl 140 0.0105 DNCN 0.05 (CTA)Br 95 0.012 DNCN 0.5 (CTA)Br 155 0.012 pNPDPPc 0.03 (CTA)Cl 75 0.07 pNPDPP 0.5 (CTA)Cl 140 0.08 pNPDPP 0.05 (CTA)Br 95 0.075 pNPDPP 0.5 (CTA)Br 155 0.085 a With a = 21 and 24 A for (CTA)Cland (CTA)Br, respectively, at 25 "C. Ks = 1600 M-I; k, = 6.4 X M-' s-l. Ks = 104 M-1; k, = 0.48 M-18-1. ~

.,

0.01

0.02

0.03

0.04

[CTACI], M

Figure2. Rsaction of pNPDPP with 0.03 and 0.5 M OH-, 0 and respectively, in (CTA)Cl. The lines are predicted (Table I).

We therefore introduced roughness into the micellar surface.22 The head group charges were assumed to have a radial distribution, g(r), about a mean position, radius a, given by a Gaussian distribution, with a coefficient, u

as shown schematically in Figure 1. We took u = 0.4 A, so that the approximate head group dispersion is f1.2 A from the average radial position, which corresponds to a = 21 and 24 A for (CTA)Cland (CTA)Br,respectively.lzbVc As in earlier work we assumed that reaction took place in a shell whose thickness A = 2.4 A. The classical equation for the electrostatic potential is now modified to include g(r):

where Zi is the valency of ion i and ni and nD are the number concentrationsof ions and head groups (ionscm-9, respectively. Equations 1-6 are combined, and we use a microcomputer to simulate rate-surfactant profiles.12 Values of a, N,and the cmc have to be consistentwith measured values, with an allowance for an increase of Nand decrease of cmc with increasing ionic c~ncentration,'~J~ and K,values are those derived earlier. Ion-specificity parameters, 6, are those used earlier, so that the only disposable parameters are u and A, which should be independent of the reaction, and k2m which should be insensitive to the reaction conditions. Nucleophilic Substitutions

As in the earliersimulationsof reactions involvingdilute OH-, C1-, Br-, s03'-, and S ~ 0 3 in ~ - cationic micelles, we took A = 2.4 A, although we also obtained reasonably good

~~

fits with A = 3 A.lzbtc Simulations for reaction of pNPDPP with dilute and moderately concentrated OH- (0.5 M) are shown in Figures 2 and 3. The fits are good in (CTA)Cl, but we underpredict kq for reaction of 0.5 M OH- in very dilute (CTA)Br (Figure 3). The fitting parameters are in Table I. The new values of kzm are similar to those estimated earlier for reactions of dilute OH-and a "smooth" micelle, which were 0.06 and ca. 0.011 M-l s-l for reactions of pNPDPP and DNCN, respectively.12b*cInclusion of the YroUghness"term, u, allows reasonable fits with modest increases of N, up to 140 and 155 for (CTA)Cland (CTA)Br,respectively, in 0.5 M OH-; i.e., the relative increase in N with increasing OH- is less than postulated earlier for reactions in up to 0.05 M OH-.lZb,c The broken linea in Figure 4 were calculatedfor a smooth micelle (a = 0) and the parameters in Table I, except that kzm = 0.012 and 0.0155 M-' 8-l for reaction of DNCN in (CTA)Cland (CTA)Br,respectively. If we accept a rough micelle (u = 0.4))we obtain fits for reaction of DNCN with 0.5 M OH-, with values of kzm that are very similar to those for reaction in dilute OH- (0.03and 0.05 M)(Table I and ref 12b). However, with a smooth micelle we fit the data reasonably well (Figure 41, provided that k p is increased by 10-25 7% in going from dilute to 0.5 M OH-. As suggested earlier,14a*b introduction of a rough micellar surface helps to explain the sharp increase in observed rate constants in micellar-assisted reactions in going from dilute to moderately concentrated OH-. Elimination We assume that N increases with increasing electrolyte concentration, but is unaffected by limited changes in

Langmuir, Vol. 8, No. 9,1992 2133

Micellar Effects in Hydroxide Ion

01

I

I

0.01

I

I

I

0.02 0.03 0.04 0.05 [CTAX], M

Figure 4. Reaction of DNCN with 0.5 M OH- in (CTA)Brand (CTA)Cl,0 and a, respectively, and in (CTA)Br + 0.05 M OH-, 0, and in (CTA)Cl+ 0.03M OH-, 0.The solid lines are predicted (Table I). The broken line is calculatedwith the parameters in Table I, except that u = 0 and kzm = 0.0155 and 0.012 M-1 s-* in (CTA)Br and (CTA)Cl, respectively. N=142 0

r

0.04-

'u)

*

x

0.02-

0.ool '

I

I

I

0.1

0.2

0.3

[OH-], M.

Figure 5. Reaction of DDT with OH- in 0.02 and 0.06 M (CTA)Br,0 and 0 ,respectively. The values of the aggregation number, N,are from eq 7.

[(CTA)Brl (c0.06M). The rate data for reaction of OHwith DDT were obtained with 0.02 and 0.06 M (CTA)Br and up to 0.3 M OH-.'" We took N = 95 and 155 for (CTA)Br in 0.05 and 0.5 M OH-, respectively, as for reaction of pNPDPP (Table I), and assumed that the increase of N followed eq 7 on the basis of the above values of N. An alternative approach is to assume a linear variation of N with [OH-], but the logarithmic form gives slightly better fits.

N = 173 + 60 log [OH7

(7)

We took A = 2.4 A, as for nucleophilic substitutions,12 although the difference between transition-state geometries for substitutions and eliminations might justify different shell widths. The question of the appropriate size of the reaction region in micelles and similar colloids has been discussedextensively,without any clear resolution of the p r ~ b l e m . ~ - ~ As J ~ noted - ' ~ ~ earlier, ~~ fits for coun(23) Hicks, J. R.; Reinsborough,V. C. A u t . J . Chem. 1982,35, 15.

terion reactions are not very sensitive to the value of A, although, as with all pseudophase models, it affects the value of kzm. The fit of the rate data is good for reactions in 0.06 M (CTA)Br,but we underpredict rate constants of reaction in 0.02 M (CTA)Brat higher concentrationsof OH- (Figure 41, on the basis of values of N given by eq 7 and kzm= 0.011 M-' s-l, which is higher than the value of k, = 0.0021 M-I s-l estimated for reaction in water.14 DDT is so hydrophobic that we assumed that reaction is wholly in the micellar pseudophase. We assumed that the aggregation number of (CTA)Br increases with increasing concentration of OH- but not of (CTA)Br. This assumption may be incorrect, because Ortega and Rodenas used a PBE model to fit data for reactions of OH- and CN-in solutions of (CTA)OH and (CTA)CN on the assumption that N increased significantly with increasing surfactant con~entrati0n.l~ In fitting the data we assumed that radii to the interfacial region do not increase with increasing concentrations of OH- and surfactant. The fits at high [OH-] (figure 4)would improve if we allowed the radius, a , to increase modestly in going from 0.02 to 0.06 M (CTA)Br, but we see no objective basis for making this adjustment. Discussion Simulated rate-surfactant profiles for reactions with moderately-concentratedOH- fit the data reasonably well (Figures 2-4). The treatment involves parameters such as N, a , A, and u (eq 1-6) that are independent of the reaction type. They are similar to values used in earlier simulations,12and are consistent with physical data on micellar size and aggregation number.24 The Volmer parameters, 6, (eq 3) are characteristic of the counterion, but we assume that they are independent of micellar size or the presence of other ions. The binding constants, KB, are substrate specific, but our substrates are so hydrophobic that fits are insensitive to the value of KB,and therefore also to the second-order rate constant, k,, in water.11J4 Our present treatment differs from that used earlier12 because we apply the concept of a rough surface. The introduction of the roughness term, u, does not appear to significantly affect fits for reactions in dilute OH-, but it improvesfits for reactions in more concentrated OH-. For the reaction of DNCN with 0.5 M OH-in (CTA)Cl,a choice of u = 0 and a higher value of kz" (Table I and Figure 4) worsened the fit. The poorest fib for substitution are with very dilute (CTA)Brand 0.5 M OH-, where predicted values of ku are too low (Figures 3 and 4). We do not know whether these results are due to limitations of the model, or to incursion of reactions assisted by monomeric surfactant or submicellar assemblies. There is evidencefor rate enhancements by nonmicellized amphiphiles for a number of react i o n ~ . ~A*pseudophase ~ ~ * ~ ~ treatment based on equations of the Langmuir form also underpredicts rate constants of reactions of DNCN and pNPDPP with OH- in dilute (CTA)Br,llbconsistent with intervention of non-micellarmediated reactions. Comparison of Pseudophase Models The classical PIE model has been modified in various ways to fit data for reactions of moderately concentrated (24) (a) Zana, R. In Cationic Surfactants; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; Chapter 2. (b)Dorshow, R. B.; Bunton, C. A.; Nicoli, D. F. J.Phys. Chem. 1983,87, 1409. (25) (a) Brown, J. M.;Darwent, J. R. J. Chem. SOC.,Chem. Commun. 1969,141. (b) Pillersdorf,A.; Katzhendler,J. Isr. J.Chem. 1979,18,330. (c) Bunton, C. A.; Bacaloglu, R. J. Colloid Interface Sci. 1987,115,289.

2134 Langmuir, Vol. 8,No.9, 1992 OH-.11J4J6-18 The modifications generally retain the concept of a distribution of counterions between micelles and water which follows a step whereas the PBE model predicta a gradual decrease of ionic concentration with distance from the micellar surface.'20*= Ionic distributions that follow the form of Langmuir isotherms fit rate data for reactions of DNCN and pNPDPP with 0.5 M OH-, which can be regarded as equivalent to an increase in /3 with added OH-." However, these ion-binding parameters may represent changes in micellar structure as well as ionic distribution, so their physical significanceis in doubt. Nonetheless, this treatment fits data under conditions in which the classical PIE model fails,and second-order rate constants of ca. 0.12and 0.018 M-ls-l for reactionsof pNPDPP and DNCN, respectively, are not very different from values given in Table I. (The comparison is based on an assumed molar volume of the reaction region of 0.14 M-l.) Another modificationof the c h i d PIE d e l involves the concept of "invasion" of the micellar reaction region, the so-called Stern layer, by ions in the aqueous pseudophase.l8Jg This invasion will be relatively unimportant in dilute electrolyte. All the pseudophase models involve disposable parameters, and data can often be fitted by selecting various values of these parameters. In the PIE model estimated second-order rate constants in the micellar pseudophase vary linearly with the molar volume of the reaction and in the PBE model they depend upon the shell width, A (eq 4). Appropriate values of the molar volume, or A, may depend upon the reaction type,23 althoughwe follow the generalassumptionthat they should not be affected by changes in structures of chemically similar reactants. Similarly,the ion exchange constant in the PIE or the ion-selectivity parameter, 6 (eq 31, should be independent of the nature of reaction. One key difference between the models is that in the PIE model the various rate and equilibrium parameters are assumed to be independent of micellar sizeand shape,3b whereas eqs 1,2,and 6 apply to spherical particles.20 The PBE model, with its emphasis on Coulombic interactions, involves the assumption that increases in electrolyte concentrationwill decreasemicellar head grouprepulsions and therefore increase micellar surface charge density. We assume that a will be constant, but the key point is that N/a2,which is proportional to surface charge density, should increase with increasing electrolyte concentrat i ~ n . ' ~ Values J~ of N and a will also depend upon the nature ofthe counterion,because weakly hydrophiliccounterions promote micellar groWth.13324 Fitting of rate data by solution of the PBE invelves assumptionsand approximations,but it provides asimple, self-consistent,physicalmodel for micellareffects on r a t a of bimolecular reactions of both counterions and co-ions. It also makes a distinction between Coulombic,nonspecific and specificmicelle-ion interactions, and with the proviso that added electrolytesincrease aggregationnumbers,lP13 it readily accomodates increaseof observed rate constants at high OH-. Values of estimated second-order rate constante, kp, in the micellar pseudophase,depend upon parameters such (26) See, for example, Figure 3 in ref 3b. (27) (a) Bunton, C. A; Mhala, M. M.;Moffatt, J. R. J. Phys. Chem. 1989,93,7851. (b)Blask6,A.;Bunton,C.A;Armetrong,C.;Gotham,W.; He,2.-M.; Nikles, J.; Romsted, L. S. Ibid. 1991,95,6747.

Bunton and Moffatt

as a, N, and A, but the key point is that fits between observed and predicted rate constants are obtained over a wide range of experimental conditions and a variety of substrates and ionic reagents.12 The treatment is also applicable to reactions of co-ions in both anionic and cationic micelles.27 The fits are generally better with (CTA)Cl than with (CTA)Br. We had noticed this difference earlier, regardless of the simulation procedure,l1JZand it is probably due to changes in structures of micelles of (CTA)Br with medium changes. These medium effects seem to be more marked with (CTA)Br than with (CTA)C1.24 Comparisonof second-orderrate constants in water and at micellar surfaces (k, and kzm, respectively) depends upon the thickness, A, of the reactive shell (eq 4)or the molar volume of the reactive region in the PIE model.2-6 Ionic concentrations in the micellar pseudophase can be written in terms of the mole ratio of ions to surfactant head groups,11but second-order rate constants then have the dimensions of reciprocal time and cannot be compared directlywith second-orderrate constants in water, k, (M-1 s-l).49k Rsgardless of the simulation procedure,l1GbJ4kzm > k, for aromatic nucleophilic substitution and elimination, but kzm < k, for dephosphorylation, and also for deacylation. These differences are probably related to charge distributions in the transition states, because negative charge tends to be localized on electronegative oxygen centers in dephosphorylationand deacylationand delocalized in aromatic substitution and elimination. Transition states with chargeslocalized on oxygen should hydrogen-bond strongly to water, but those with delocaliid charges should interact more readily with cationic surfactant head groups. Experimental Section The rate constants are literature values, at 25.0 "C, and values Values ~ J ~of a and N in of k, and K,are from earlier ~ o r k . l ~ & dilute OH- and the ion-specificity Parameters, 6, are similar to those used earlier.12 As in earlier work, the radius, a, to the charged surface is lower than the hydrodynamic radius of the micelles which includes contributions of methyl groups and associated counterions and water molecules.24 We neglect contributionsof submicellar assemblies,and we do not explicitly consider micellar size dispersion. Second-order rate constants ~ ~ Jwith ~ our hydrophobic in water, k,, are literature v a l u e ~ , but substrates, reactions in water make only minor contributions to the overall fiit-order rate constanb, ky. The binding constant, K,,of DDT in (CTA)Br was taken as 2000 M-l without added electrolyte,but it was assumed to increase significantlyin NaOH due to "salting-out"of DDT.'" We therefore assumedthat DDT would be more than 99 9% micellar-bound in 0.02 M (CTA)Brand added OH-; cf. ref 14a,b. The concentration of monomeric surfactant is assumed to be the critical micelle concentration, cmc, under kinetic conditions." Added electrolytes reduce the cmc, and we take values used earlier to fit data for reactions of DNCN and pNPDPP.IIb The fits are unaffected by values of these 'kinetic" cmc except for reactions of DNCN and pNPDPP in dilute surfactant (Figures 2-4). Simulations were carried out on PC microcomputers as described earlier,12with parameters given in Table I.

Acknowledgment. Support of this work by the National Science Foundation (Organic Chemical Dynamics Program) and the U.S. Army Office of Research is gratefully acknowledged. Registry No. (CTA)Cl, 112-02-7; (CTA)Br, 57-09-0; p NPDPP, 10359-36-1; DNCN, 2401-85-6; DDT, 50-29-3.