11324
J. Phys. Chem. 1993,97, 113 2 4 1 1331
A Nuclear Magnetic Resonance Study of Ion Exchange in Cationic Micelles. Successes and Failures of Models Andrei Blask6, Clifford A. Bunton,. Giorgio Cericbelli,' and Don C, McKenzie Department of Chemistry, University of California, Santa Barbara, California 931 06 Received: May 18, 1993; In Final Form: August 18, 1993@
The displacement of B r or C1- from cetyltrimethylammonium ion micelles by added anions can be monitored by following changes in line widths of 7 9 B r signals or line widths or chemical shifts of 35Cl- signals. Tosylate ion displaces B r very strongly from micelles, and displacement by NO-3, N-3, C1-, and HCO-2 is fitted by the pseudophase ion-exchange (PIE) model. This model fails for addition of OH- or F- to (CTA)Br, and of OHto (CTA)Cl, but the displacement is fitted by the Poisson-Boltzmann equation (PBE). A rationalization is given for the ability of the PIE model to fit kinetic data for reactions of OH- in micellized (CTA)Br or (CTA)CI even though it does not fit the N M R data.
Propertiesof aqueoussurfactant assemblies are very dependent upon the nature of the counterion. For example, critical micelle concentrations, cmc, decrease, and hydrodynamic radii and aggregation numbers increase, as counterions become less hydrophilic.2 There are analogies between interactions of counterions with ionic micelles and with ion-exchange resins, and strongly-boundcounterions displace weakly-bound ions.3Rate enhancementsof bimolecular reactionsby micelles are due largely to their ability to concentrate both ionic and apolar reagents at their surfaces.3.4 Added inert counterions reduce micellar rate effects by competing with reactive ions for these surfaces, and this competition is also important for reactions mediated by vesicles5 and microemulsions.6 Rate effects of micelles and similar colloidal assemblies are therefore generally described in terms of a pseudophase model with water and micelles regarded as distinct reaction region^.^,^^^ The overall reaction rate is the sum of the rates in each pseudophase and depends upon the rate constants and reactant concentrations in each pseudophase. Reactions of OH- in cationic micelles or similar assemblies are well studied, as are inhibitions by inert anions that compete with OH-. Reactive ion concentrations at micellar surfaces can sometimes be estimated directly, for example, electrochemically,* by fluorescence q~enching,~ by changes in NMR spectra,lo or by trapping of aryl cations in dediazonization,l*but these methods are not applicable to OH-. However, various theoretical models have been reasonbly successful in fitting rate effects of ionic surfactants and added electrolytes, in terms of the transfer equilibria of ionic and nonionic solutes.3-4J2-16 ' The pseudophase ion-exchange model (PIE) has been used extensively. It is based on two related key assumption~:33~h (i) the micellar fractional charge, a,is constant, and (ii) counterions exchange on a 1:1 basis, according to eq 1,as shown for competition
between OH- and B r in micellized cetyltrimethylammonium bromide ((CTA)Br, Cl6H33NMe3Br). Similar equations are written for other pairs of ions. In eq 1, the quantities in squared brackets are molarities in terms of total solution volumes and subscripts W and M denote aqueous and micellar pseudophases, respectively. Thus, B r , or another inert anion, inhibits micellar-assisted reactions of OHa Abstract
published in Aduance ACS Abstracts, October 1, 1993.
0022-3654/93/2091-11324%04.00/0
by excluding it from micellar surfaces and this principle also applies to micellar effects upon equilibria involving OH-.3b Micellar rate effects on bimolecular reactions of OH-, for example, can be fitted in terms of the concentrations of OH- and the substrate in the aqueous and micellar pseudophases and the appropriate second-order rate constants. For reactions of OHin (CTA)Br, we can write the concentration of OH- as a mole ratio of the micellized surfactant:
m 0 2 = [OH-,]/([(CTA)Br]
- cmc)
(2) where the critical micelle concentration, cmc, under kinetic conditions, gives the concentration of monomeric surfactant.' The distribution of substrates between water and micelles can be measured directly, or estimated,3~4JZbut that of OH- has to be calculated, for example, in terms of eq 1. Provided that fractional micellar ionization, a,or neutralization, 8, is constant (B = 1 - a),the concentration of OH- (or another ion) in the micellar pseudophase is given by eq 3, or equations of similar general form.3v4"*5J3 Subscript T denotes total concentrations.
(mOHS)2
+
(e:-
1)( [(CTA)Br] - cmc)
-6)-
[OH-,]@ = 0 (3) - l)([(CTA)Br] - cmc)
(g:
Equation 3 can be used to predict variations of first-order rate constants, k$,with concentrations of surfactant and reactive or inert ions. This treatment fits a great deal of kinetic and equilibriumdata and explains effects due to changes in surfactant and reactant concentrationsand in substrate hydrophobi~ities.3.~& Equation 3 can be rewritten in terms of the mole ratio of the inert counterion to micellized surfactant, mBrSor mas, for B r or C1-, respectively. The fitting of rate data by the PIE has been extensively discussed,334has have the limitations of the treatment, including the assumed constancy of a and the quantitative failure at high ionic concentrations.aJk18 Values of applied to reactions of OH-in solutions,typically of (CTA)Br, vary over a wide range, e.g., 10-50, and it is not clear what is the 'best" value. However, B r , for example, is very effective in displacing OH- from the surface of a cationic micelle, and anion affinities seem to follow a salt order OTos- > NO3- = B r > C1- > OH- akin to the Hofmeister series.3-4b+-c,9J3Equation 1 predicts that OH-, in high concentration, should displace B r from a cationic micelle, but fluorescence quenching shows that OH- and F- are much less 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11325
An NMR Study of Ion Exchange in Cationic Micelles
I
I
2
I
4 [ NaX]/[CTABr]
1
I
6
8
I,
I
10" 20
I
I
40
[NaZSO4]/[CTABr]
Figure 1, Effects of anions on the line width of T9Br in 0.05 M (CTA)Br: 0,OTOS-;0 , NOo-; 0, N3-; 0 , C1-; m, OH-; SO,'-.
+,
effective in this role than expected in terms of typicial values of the ion-exchangeparameter (eq l).9 In addition, the PIE model appears to fail for mixtures of very hydrophilic anions,19 and other problems with the model have been noted.3.4k.20 Other models have been applied to interioniccompetition. For example, micelle-ion interactions can be described by equations with the form of Langmuir isotherms, without assumptions on a.14,21 Alternatively, competition can be treated by solving the nonlinear Poisson-Boltzmann equation (PBE) on the assumption that ions interact both Coulombically and specifically with ions.15J6v22 However, the PIE model is the most widely used treatment of micellar effects upon reaction rates and eq~ilibria.39~~ Line widths of NMR signals of 79Br, 81Br, and 35Cl- broaden markedly due to interaction with tetraalkylammonium i0ns,~3 and this method has been used to follow the distribution of B r and C1- between water and cationic micelles.10~24~25 We planned to use it to examine displacement of B r and C1- from CTA+ micelles by anions of varying polarizability and hydrophilicity and totest thevalidityofeq 1 andother treatments. Thisapproach has limitations, especially for B r , because its NMR signals are very broad and it is difficult to obtain good values of line widths in micellar solutions. However, the measurements improve as B r is displaced from the micelle and lines sharpen. The method fails if micelles become rodlike, the solutions become viscous, and signals broaden.2s Transfer of B r (or Cl-) between water and micelles is fast on the NMR time scale, and the line width, B, (of B r ) is given by B[Br-,] = B,[Br-,]
+ &[B~-M]
(4) A similar equation can be written for changes in chemical shifts (CS), although it is difficult to measure them with the very broad signals of B r . Both B and CS can be followed with the sharper signals of Wl-. For convenience we consider equations for the distribution of B r . but treatments are similar for C1-.
Results Qualitative Observations on (CTA)Br. We first used 0.05 M (CTA)Br in H20:D20 4 1v/v at 25 "C and found that the behavior of added anions followed three approximate patterns (Figure 1): (i) Moderately hydrophilicanions appeared to displace B r from the micellar surface, and values of B fell smoothly toward a value of ca. 500 Hz, characteristic of '9Br in water. (ii) Initial addition of OTos- initially increased B, probably because OTos- causes a sphere-to-rod transition manifested by a marked increase in the viscosity of aqueous (CTA)Br,25,26but then B fell very sharply as B r was almost completely displaced from the micelle. (iii) Very hydrophilic anions, OH- and S042-, initially decreased B, but its value then decreased only slightly and even high
I
I
I
I
I
I
I
0.4
0.2
I
I
I
0.6
0.8
1N O X I , M
I
1 .o
Figure 2. Effectsof anions on the line width of '9Br in 0.01 M (CTA)Br + 0.01 M NaBr: 0 ,NO,-; 0, N3-; 0 , Cl-; HC02-. The upper and lower solid lines are calculated with Ktr = 6 and 1.2, respectively, and the broken line with Kg, = 4. Insert gives data for OTos-, 0.
+,
9 t
3t1
"
I
I
0 I
I
'
1
l
l
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 [Oi],M, [F-1 ,M. Figure 3. Effects of OH- and F- on the line width of '9Br in 0.02 M (CTA)Br: 0 , OH-; H, F-. Open points, 0 denote values simulated by
the PIE model with g: = 15. The lines are simulated by the PBE: -, A = 2.4 A; - -, A = 2.4 A, u = 0.4;- - -,A = 4 A, a specificity parameter for F-, see text, and N = 100 and (I = 25 A.
-
concentrations of OH- and S042-did not displace B r completely from the micelle. We did not attempt to treat these data quantitatively because they had poor reproducibility, even without added salt, and micellar shape and increasedviscosity was a complicationin some conditions. Measurements on Dilute (CTA)Br. We next examined the effects of addition of NOg, N3-, C1-, HC02-, and OTos- to 0.01 M (CTA)Br 0.01 M NaBr where lines should be sharper, and micellar growth less of a problem, than with 0.05 M (CTA)Br. However, addition of 0.01 M NaBr decreased the sensitivity of the measurement. The results are qualitatively similar to those shown in Figure 1, except that Bdid not increaseon initialaddition of NaOTos. With large excesses of N03- and N3-, values of B decreased toward that of 79Brin water and even dilute OTosmarkedly decreased B (Figure 2). We finally concluded that 0.02 M (CTA)Br gave reasonbly good data and examined addition of OH- and F- (Figure 3). Qualitatively, the results are similar to those obtained with 0.05 M (CTA)Br (Figure 1) in that even a very large excess of OHdoes not displace B r extensively from the micellar pseudophase. Measurementswith0.05M (CTA)Cl. Linewidths of theNMR signals of 3 x 1 - can be measured readily in 0.05 M (CTA)Cl, and we examined the competitionbetween C1- and OH-. The behavior is very similar to those observed with (CTA)Br, and line widths tend toward limiting values that are much higher than that of 8 Hz in water (Figure 4). We were also able to monitor changes
+
Blask6 et al.
11326 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993
[BI-M] or mg3.15,16,28Allowance is made for the concentration of monomeric surfactant, which is generally taken as the critical micellar concentration, although its value falls sharply on addition of salt and becomes negligible. Variations of the chemical shift (CS, ppm), referred to 3sClin water, are given by
0
120 0
loolk
1 4 1
0
cs = CsM [Cl-M] / [Cl-,]
(7) where CSM is the chemical shift of 3sCl- in the micellar pseudophase. It is significant that results with (CTA)Cl + OH- are very similar whether they are based on changes in line width, B, or chemical shift (Figures 4 and 5). This agreement shows that eqs 4-6 are reasonablysatisfactory in describingdistributionsof halide ions. Data which are treated quantitatively are shown in Figures 2-5.
I
40t I
20
Discussion
b
0
I
I
I
I
I
I
1
The PIE Model. The decreases of the line widths of B r on addition of OTos-, NO3-, N3-, C1-, and HC02- follow the sequence found for salt effects upon micellar-assisted r e a c t i o n ~ . ~ , ~ ~ J Values of the mole ratios of bound anion to micellarizedsurfactant (moHS, mB3, or their equivalents for the other ions) can be calculated by solving eq 3, or its equivalent, for the given pair of anions, with selected values of /3 and the ion-exchange parameter (eq 1). This treatment is described in detail for various values of these parameters in kinetic treatments.3.4bJ3 There are various ways of defining /3 (or and reported values depend upon the method of determination. The simplest way to apply the PIE model to these data is to estimate BMfrom the line width B of a solution of 0.01 M (CTA)Br 0.01 M NaBr with a reasonable value of /3 and the known line width in water, BW (eqs 4-6). For (CTA)Br we took 8 = 0.8 and B r w = 500 Hz (Experimental Section), which gives BM = 16 000 Hz. We then calculated [ B ~ Mand ] [Brw] in terms of various values of the ion-exchange parameter K;! (eq l), where X-is the added anion, and used these concentrations with values of BMand BWto predict the decrease of the experimental line width, B, with added salt (eq 4). The fits are reasonably good for added NO3-, N3-, Cl-, and HCOz- (Figure 2) on the basis of ion-exchange parameters Kir = 1.2 for NO3- and N3- and 6 for C1- and HCO2-, which are similar in magnitude to accepted values.3.4k A value of Kir = 4 also fits data in dilute C1- and HC02- (Figure 2, broken line). The fits are not very sensitive to small changes in /3, BM,or the ion-exchange parameter (eq 1) for competition between B r a n d the added anion. The fit for C1- and HC02- deteriorates at high salt, and the results could be interpreted on the assumption that the ion-exchange parameter increases in favor of B r at high added salt, cf. ref 11. We did not attempt to fit data for NaOTos because it very stronglyperturbs the micellar structure and appears to exclude other anions almost completely from the micellar pseudophase.26 The PIE model is satisfactory when B r and the added anion have similar affinities for the micelle, but we could not fit the data for competition involving OH- or F- in (CTA)Br or OHin (CTA)Cl. This failure is illustrated in Figures 3-5 where the open points are calculated by the PIE treatment. For 0.02 M (CTA)Br (Figure 3), we took = 15, which is typical of values used to fit kinetic data, but predicted line widths are too high in dilute OH- and too low in more concentrated OH- (open diamonds). If we select a lower value of that fits the data in dilute OH-, the fit becomes even worse at higher [OH-]. The fit is slightly better for addition of F-, with Kir = 15, but even then in dilute F- the predicted value of B is too high and it is too low at high [F-1.
+
I
u .-. _ -
0
-.-.
0 b
2t
Q 6
I
I
I
0.2
I
I
0.4
I
I
I
0.6
I
A
l
0.8 y1.85
[OR], M Figure 5. Effect of OH- on the chemical shift of W 1 - in 0.05 M (CTA)C1. Symbols are as in Figure 4.
in the chemical shifts of 3sCl- on addition of OH- to 0.05 M (CTA)Cl (Figure 5). Micellar growth is much less of a problem with (CTA)Cl than with (CTA)Br.25927 QuantitativeTreatments. Equation 4 can be applied in several ways, for example, with concentrations written as in eqs 5 and 6, and we consider the use of the PIE treatment (eqs 1-3)3J3 and [&-MI = m,,S([(CTA)Br] [Br-,]
- CmC)
= [(CTA)Br] - [ B i M ] + [NaBr]
(5)
(6)
also the nonlinear Poisson-Boltzmann equation for estimation of
e:
An NMR Study of Ion Exchange in Cationic Micelles
The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11327
The situation is similar for addition of OH- to (CTA)Cl as (esu), t the dielectric constant of water, k Boltzmann’s constant, shown in Figures 4 and 5 (open squares or diamonds), and we and Z i the valency of ion i, and ni and nD are the number took a = 0.25 (B = 0.75). The data in dilute OH- could be fitted concentrations of ions and head groups (ions ~ m - ~respectively. ), The term nDg(r) allows for surface roughness, and head group by an ion-exchange parameter between 5 and 15, but it would havetobemuchhigherthan 15tofit thedatainmoreconcentrated charges are assumed to have a radial distribution at the surface OH-. The data for both (CTA)Br and (CTA)Cl could be fitted about themean position, radius a, given by a Gaussiandistribution, by the PIE treatment if we allowed the ion-exchange parameter with a coefficient u18 to increase very strongly with increasing [OH-] or [F-1, but it is difficult to rationalize such an increase, and predictive power is (9) lost. One limitation of the PIE model is the assumption that a,(1 Equation 8 is solved by numericalintegrationwith the boundary - B), is constant, because a for (CTA)Br is ca. O.2?J whereas conditions for (CTA)OH it is much higher, Le., ca. Therefore the PIE, with interionic competition, predicts that a should increase $ = d $ / d r = O at r = R (10) on addition of OH- to (CTA)Br (or (CTA)Cl). But a higher a implies decreasedcounterion concentrations at micellar Surfaces, d$/dr = (1 -j)Ne2/Ea2kT at r = a (1 1) whereas we see less loss of halide ions than predicted by the PIE, so adjusting the value of a does not improve the fit. We conclude where f is the fractional specific coverage by counterions which that the PIE model (eq 1) does not describe displacement of leads to neutralization of the charge of an equivalent number of micellar-bound B r or C1- by OH-or F, except in dilute electrolyte, head gro~ps.15b.~ although the treatment appears to describe displacement of OHIf only one specifically-interactingion is present, we writefin by B r or C1- on the basis of analysis of kinetic and equilibrium terms of a Volmer isotherm (shown for B r ) data with relatively dilute We also examined a treatment in which ionic transfer between water and micelles is described by equations of the form of Langmuir isotherm^.^^.^^-^^ This treatment fits kinetic data for reactions in aqueous and alcohol-modified micelles at concenand the micellar surface charge density is modified accordingly trations of OH-for which the PIE treatment fails. However, this (eq 11). treatment does not fit the NMR data on the displacement of B r When two specifically-interactingions are present, we use the or C1- by OH- and is essentially no better than the PIE treatment simpler Langmuir isotherm (eq 13). as applied to this problem (fits not shown). The PBE Model. The results considered so far show that the PIE model fits the line width data for 79Br provided that the competing anion is not very hydrophilic, but it fails for very hydrophilic anions, except when they are dilute. We therefore The two isotherms are equivalent at low coverage, and the considered an alternative model in which ions such as B r , that specificity parameters, 6, differ by a factor of 2.33 The specificity are polarizable and not very hydrophilic,interact with the micelle parameter 6 (eqs 12 and 13) is zero or very small for hydrophilic, both Coulombicallyand by a specific, non-Coulombicattraction, high charge density ions and larger for bulky, polarizable ions. which allows B r , for example, to intercalate the micellar surface Values of 6~~ = 120 and 15 M-1 were used earlier in fitting and to neutralize the charge of an equivalent number of head kinetic data on the basis of eq l2.15b,c Values of N and a are groups.15bqc.22 A strongly hydrophilicanion, e.g., OH-, is assumed known from independent evidence, and the fitting procedures to interact only Coulombicallywith the micelle. On this model, have been d e ~ c r i b e d . ~ For ~ J ~kinetic work, we estimate the B r competes with OH-by entering the micellar surface and concentration of a reactive ion, e.g., OH-, in the reactive shell, reducing its charge density, and therefore the surface electrical thickness A, but in the present work, we are interested in the potential. This effect is in addition to a normal nonspecific concentrations of B r , rather than OH-, at the micellar surface. electrolyte effect on the surface electrical potential.15J6J8 On The kinetic data for anionic reactions in solutions of cationic the other hand, OH- does not neutralize head group charge but micelles were fitted with A = 2.4 A.15 Kinetic fits are not very merely exerts an electrolyte effect upon the surface potential. sensitive to small changes in A, although the derived secondThis treatment successfully predicts ratesurfactant profiles for order rate constant in the micellar pseudophase depends on A. reactionsof several anionsin solutions of cationicsurfactants15J6J8 In the present work, we initially took A = 2.4 %I and u = 0 (eq of OH-in solutions of sodium dodecyl sulfate, SDS,” and of 9), Le., for a “smooth” micelle, as for reactions of dilute H30+ in (CTA)C1.32 nucleophilic anions.15 We also made calculations with A = 4 A The distribution of ions around a spherical ionic micelle is and u = 0 and with A = 2.4 A and u = 0.4 (for a “rough” micelle) calculated in terms of the cell model15J6.28 by solving the PBE without materially changing the fits for (CTA)Br (Figure 4). in spherical symmetry with allowance for specific interactions which allow B r or C1- to intercalate the micellar s ~ r f a c e . ’ ~ , ~ ~The calculationswere made with BM= 14 000 Hz, which is slightly lower than the value used in fitting data by the PIE model, and The variations of potential and ionic concentration with distance we took Bw = 500 Hz (Experimental Section). from the micellar surface are calculated, and average ionic Wedid not apply the PBE to competition involving moderately concentrationswithin a shell of assumed thicknessat the micellar hydrophilic anions, e.g., NO3-, N3-, C1-, and HC02-, because the surface are then c a l c ~ l a t e d . ~ ~ J ~ - ~ ~ simpler PIE model adequately fits the data (Figure 2). The PBE The original kinetic treatment was given for a smooth,spherical model fits micellar effects upon S Nreactions ~ of B r (and C1-) micelle of radius a, and aggregation number N in a cell, radius and describes competitionbetween Brand MeSO3-.Ik However, R,and it was modified for a rough micelle:l8 any competition model should fit the data when the two ions have similar affinities for micelles. - d(rz d’/dr) = - e ( c Z i n f exp(-Zi$) n d r ) ) (8) The fits for line widths and chemical shifts in (CTA)Cl are 2 dr tRT reasonable, and variations in A and introduction of a roughness term do not have major effects (Figures 4 and 5 ) . For (CTA)Cl where r$ is the reduced potential, r$ = e+/kT, $the electrostatic we tookslightlydifferent values of BMand CSMfor W l - depending potential, T the absolute temperature, e the electrostatic charge
+
11328 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 TABLE I: Fitting Parameters and the Effect of an Increase in IV (CTA)Br (CTA)Cl [OH-], M N [BTMI/ [BTTI N [chi/ [cl-~l 100 113 142 167 192
0.1
0.3 0.8 2.0
0.57 0.44 (0.43) 0.42 (0.42) 0.42 (0.42) 0.41 (0.41)
90
0.56
103
0.37 (0.36)
151 175
0.29 (0.29) 0.28 (0.18)
Calculated with a = 25 and 21 A for 0.02 M (CTA)Br and 0.05 M (CTA)Cl, respectively, A = 2.4 A, and Volmer parameters, 6, of 0, 15, and 120 M-I for OH-, CI-,and B r , Values in parentheses are for constant N of 90 and 100 for (CTA)CI and (CTA)Br. 0
upon the fitting parameters (Figures 4 and 5 and Experimental Section). Fits are not very sensitive to these changes. The treatment of the effect of F- upon the line width of 79Br in (CTA)Br is also fitted reasonably well. The effect of F- is larger than that of OH-, and in fitting the data, we took a nonzero value of 6 ~eq . 13. We use a Langmuir rather than a Volmer isotherm (eqs 13 and 12,respectively) with = 60 and 6; = 1 M-1, corresponding to Volmer parameters of 120 and 2 M-I, respectively, in eq 12. The fits shown in Figures 3-5 were made with constant values of the aggregation number N . Added salts increase micellar aggregation numbers, and fits of data for reactions of moderately concentrated OH- in (CTA)Cl and (CTA)Br improve if we assume that N increases with increasing [OH-]. we, therefore, resimulated the variation of B with OH- in 0.02M (CTA)Br and 0.05 M (CTA)Cl with N increasing, as had been assumed for kinetic fits for reactions of OH-.18 There is a negligible effect (Table I) because the micellar binding of B r is governed largely by specific interactions which, except in dilute electrolyte, are much more important than the Coulombic interactions and, in our approximations,are size independent.15 However, Coulombic interactions with OH- are all important, so simulationsof kinetics of its micellar-mediated reactions should be sensitive to aggregation numbers.13.16.18.28 The PBE model based on the parameters given in Table I predicts the qualitative forms of plots of line width B or chemical shift against the concentration of added hydrophilic anions, particularly the initial relatively sharp decrease and subsequent leveling-off of B, regardless of values selected for such fitting parameters as aggregation number, N, shell width, A, and a %mooth” as compared with a urough”micelle (Figures 3-5). The calculation gives values of ionic concentrations averaged over a shell of width A, which we take as 2.4 or 4 A. Romsted and co-workers are using dediazonization and the trapping of phenyl cations to estimate surface concentrations of weakly basic nucleophiles in cationic micelles.” The estimated concentration of B r at the surface of a (CTA)Br micelle depends to a minor extent upon the diazonium ion probe. With one probe in 0.01 M (CTA)Br 0.1M HBr, the estimated interfacial concentration of B r is 3.3 M,“b but with a different probe in 0.01 M (CTA)Br + 0.01 M HBr, the concentration is 2.3 M.lla The calculated concentration also depends upon the system used to monitor the referencereaction in water.34 Under slightly different conditions, 0.02M (CTA)Br and no added B r , we calculate concentrations of B r of 3.5 and 2.8M averaged over 2.4 and 4 A, respectively. While this agreement is encouraging, we note that the calculated concentrations depend upon assumed values of parameters such as A and they may not be appropriate for the dimensions of the interfacial region sensed by dediazonization. We considered whether some of the approximationsin the PIE model are responsible for its inability to fit our NMR data. The PIE model involves the implicit assumption that the micellar pseudophase, often identified with the Stern layer, is a region distinct from bulk water and that ionic distribution can be written
Sir
+
Blask6 et al. as a step function.394.7 This approximation is reasonable in dilute electrolyte where ionic concentrations at the micellar surface are higher than in water by orders of magnitude, but it becomes less satisfactory at high concentrations of electrolyte, and rate constants at high [OH-] are larger than expected in terms of a constant value of ( Y . ~ C + J ~ . J ~ , ~ I In order to explain these high rates, it has been suggested that counterions from water Ynvade” the micellar pseudophase,35 but it is not clear how this concept helps to explain our NMR data because *invasion”by OH- should not increase concentrations of B r or C1- at the micellar surface. Coulombic treatments of ion binding predict that there will be a smooth distribution of ions between the micellar surface and bulk solvent, or the cell wall in thecell model.14J5*28 If we include specific binding, as for C1- or B r (eqs 12 and 13), some ions will intercalate the surface and others will be very close to it and calculated concentrations of micellar-bound ions depend upon the shell width, A. Ions, such as OH-, which are assumed to bind only Coulombically, will not intercalate the surface, but their concentration in a shell of width A will increase with their total concentration in that region. However, this concentration effect will be attenuated with ions such as B r a n d C1- which interact specifically with the micellar head groups and their surface concentration will not increase very sharply with their total concentration or the magnitude of A. In fitting the NMR data by the PBE model, we considered different values of the shell width, A, and allowed BMor CSMto change modestly (Experimental Section) and we do not claim to have selecteda “best fit” simulation. The significant point is that the model predicts both the initial sharp drop of B or CS on addition of OH-, or F-, to (CTA)Br or (CTA)Cl and the subsequent leveling-off at higher anion concentrations. The parameters used to fit the NMR data are very similar to those used to fit kinetic date for reactions of OH-, C1-, and Br,lsb.c although we do not claim that the values of these parameters are uniquely correct. W h y Does PIE Fit So Mucb Kinetic Data? The PIE model does not describe displacement of B r or CI- from micelles by very hydrophilic anions, e.g., OH- or F-, but it satisfactorily fits rate-surfactant profiles for reactionsof OH- in solutionsof cationic surfactants, e.g., (CTA)Cl or (CTA)Br.3s4hJ3 It also describes effects of inert anions on these reactions, and although there is less evidence on reactions of hydrophilic cations, e.g., H30+, mediated by anionic micelles, the PIE model generally fits these data, at least in dilute acid.36 We have the paradox that the PIE model seems to describe displacement of OH-,for example, by less hydrophilic ions, but not the reverse displacement, although the basic ion-exchange equation (eq 1) should describe equilibrium distributions of the two ions between aqueous and micellar pseudophases. However, trapping experiments show that the ion-exchangeparameter (eq 1) for moderately hydrophilic ions (Cl- and B r ) is not strictly independent of ionic concentration.11 The rate equation for a micellar-assisted reaction of OH- with a nonionic substrate, S, in solutions of (CTA)Br is kJ. =
kMKSmoHS([(CTA)Br]- cmc) (14) 1 + Ks([(CTA)Br] - cmc)
kw[OH-,]+
where k+is the observed first-order rate constant, kw is the secondorder rate constant in water (M-] s-l), kM (s-I) is that in the micellar pseudophase with the concentration of OH- written as a mole ratio, mOHSwith respect to micellar head groups, and KS is the binding constantof the substrate to micellized s~rfactant.3.~.l2 The second-order rate constant in the micellar pseudophase can alternatively be written with concentration as a molarity, i.e. k,“ = kMVM (15) where VM(M-1) is the molar volume of the reactive region. This
An NMR Study of Ion Exchange in Cationic Micelles
The Journal of Physical Chemistry, Vol. 97, No. 43, 1993 11329
I
I
I
0.01
I
I
I
[CTABr], M
Figure 6. Simulated ratesurfactant profiles for hypothetical reaction of OH- in (CTA)Br with constant k~ (s-l) and indicated values of ranging from 10 to 50. The insert shows the simulation for dilute (CTA)Br.
region is sometimes identified with the whole micelle and sometimes with the volume which encompasses the head groups.394J3 Equations 3 and 14 are combined, and the variation of k+with [OH-], [(CTA)Br], or [ B r ] can be predicted in terms of the rate and equilibrium constants in eqs 3 and 14 and @ and the cmc. For relatively hydrophobic substrates, most of the reaction occurs in the micellar pseudophase and fits are relatively insensitive to values of KSand the cmc, although generally the latter is assumed to be lower than that in the watera3q4As regards the other parameters in eq 3, the value of @ almost certainly depends upon the nature and concentration of added counter ion^.^^ The failure of the PIE treatment with reactions of moderately concentrated reactive ion is sometimes ascribed to an increase of @ at high [electrolyte],17but the problem is thought to be less serious at low ionic concentrations. It is more difficult to select the appropriate value of the ionexchange parameter, or even to decide if there is such a value, and values of that have been used to fit kinetic data very markedly. We simulated variations of k4 with [(CTA)Br] up to 0.05 M for a hypothetical reaction of 0.01 M OH- with a moderately hydrophobic substrate, KS = lo3 M-I. These values and conditions are typical of those that apply to many micellarassisted bimolecular reactions. For simplicity, we took cmc = 0 and @ = 0.8, which are similar to accepted value~.39~&The calculations were made with kw = 0.01 M-l s-l, and initially we calculated the rate-surfactant profiles with kM = 0.01 s-l and varied g y between 10 and 50. The predicted curves of k+ against [(CTA)Br] are very different (Figure 6 ) , but this result is uninformative because in a real experiment we would have no way of knowing the value of kM, unless we could measure the transfer equilibrium of OH- between water and the micelles by some independent method. In Figure 7 we show plots of k+against [(CTA)Br] with varying values of KM, which are 0.01, 0.015, 0.02, and 0.03 s-1 corresponding to equaling 10,20,30, and 50, respectively. The predicted curves are now essentially indistinguishablewith [(CTA)Br] > 5 X M, bearing in mind experimental errors in rate constants. The curves differ at the rate maxima, which are at [(CTA)Br] = 1 6 3 M, but in practice it is very difficult to predict positions of rate maxima because they depend upon Ks and the concentration of the monomeric surfactant, both of which may be affected to an unknown extent
g7
I
I
I
I
0.02 0.03 0.04 0.05 [CTABr], M
I
0.02 0.03 0.04 0.05
I
0.01
Figure 7. Simulated rate-surfactant profiles with the following combinations of and kM (s-l), respectively: solid line, 10,O.Ol s-I; - - -, 20, 0.015 s-I; - -, 30, 0.02s-I; ., 50,0.03s-l. The error bar is &5% at the rate maximum.
e: e
--
by the reactants. For example, we generally assume that the cmc gives the concentration of the monomeric ~ u r f a c t a n t , ~but . ~ .both ~ electrolytes and hydrophobic solutes decrease the ~mc,3.~’ so a “kinetic cmc” is generally taken as a disposable parameter, with consequent uncertainties in the predicted fits in dilute surfactant. An additional, widely recognized problem is that submicellar assemblies may also assist the reaction.3* It is therefore difficult to predict positions of rate maxima for bimolecular reactions of moderately hydrophobic substrates, and they would change markedly in our theoretical plots (Figures 6 and 7)if we modestly increased the cmc to 8 X 10-4 M,Le., to the value in the absence of added electrolyte. Therefore, although in principle it should be possible to test the treatment by examining the rate-surfactant profile under conditions in which the substrate is only partially bound, the fit then depends very much upon the assumptionsthat the monomeric surfactant and submicellesdo not affect the rate and, for weaklybound substrates, that KS and the cmc are unaffected by added ions. In addition, if the surfactant is not in large excess over the substrate, perturbation of the micelle by the substrate may invalidatethe assumptions regarding micelleion interactionsthat are implicit in the PIE and in other pseudophase treatments of ionic reactions. Another way of considering limitations of the PIE treatment is to examine limiting conditions of dilute OH- with [(CTA)Br] well above the cmc where OH- will be largely in the water, Le., [OH-w] = [OHTI and [ B r ~ ] / [ B r w ]= (1 - a ) / a ,and eq 1 is approximated by
For the fully-bound substrate and [(CTA)Br] gives
>> cmc, eq
14
Under these limiting conditions and constant a,the observed first-order rate constants will vary linearly with [OH-T] and inversely with [(CTA)Br], regardless of values selected for a and the ion-exchange constant, The situation is not helped by using an all-obliging microcomputer to predict the “best fit”. Values of Ks,@, and the
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e:,
11330 The Journal of Physical Chemistry, Vol. 97, No. 43, 1993
concentration of the monomeric surfactant may change with concentrations of the surfactant and reactants, and fits a t low and high [surfactant] depend differently upon the various parameters in eq 14. Despite our reservations regarding the quantitative application of the PIE model to reactions of hydrophilic anions, we believe that it is descriptiviely very useful in explaining many features of micellar-mediated bimolecular reactions. In addition, the approximation which lead to eqs 16 and 17 will not be applicable for ions that compete effectively with the surfactant counterion, Le., when the ion-exchange constant (eq 1) is not very different from 1. This situation should apply to reactions of moderately hydrophilic anions$b e.g., CN- or N3-, in solutions of (CTA)Br or (CTA)Cl, especially if ion-transfer equilibria can be followed by physical or chemical measurements and a (0) is essentially unaffected by ion-exchange, and here fits to the PIE model should provide a good test of its validity. The ion-exchange parameter for competition between H30+and Na+ appears to be ca. 1, on the basis of electrochemical data with anionic micelle^,'^ so here kinetics provide a more critical test of the PIE, at least in dilute solutions.36 These questions regarding the applicability of the PIE treatment apply to the behavior of other colloidal assemblies where the PIE treatment has been applied, e.g., microemulsions,6 vesicles,S nucleic acids,Na and polyelectrolytes.4Ob A rationalization for the ability of the PIE model to fit competition between moderately hydrophilic ions is that micelleion interactions involve both nonspecific, Coulombic and specific forces. The PIE model factors out the role of Coulombic forces, so one is left with the ion-specific forces which are described adequately by the ion-exchange e q ~ a t i o n . ~ This - ~ ~ rationalJ ization fails with very hydrophilic ions where interactions are dominated by Coulombic forces,lg but for systems in which the PIE model is applicable, it is reasonable to use a simple, rather than a complex, quantitative treatment. As pointed out originally by Romsted, the PIE model is satisfactory provided that a is insensitive to the nature of the counterion, because ion-exchange is then on a 1:l basis.3 It appears that if we exclude very hydrophilic anions from consideration both the PIE and the PBE models describe interionic competition reasonably well. The competition between B r and C1-, HCOz-, NO3-, or N3- in 0.01 M (CTA)Br 0.01 M NaBr is fitted by the PIE treatment (Figure 2), and the PBE model has been used to fit kinetic data for S Nreactions ~ of B r and C1- in the presence and absence of inert anions.lSc Equations which write transfer equilibria in the form of Langmuir isotherms also fit kinetic data for reactions of nucleophilic anions in the presence and absence of inert anions and are applicable to anionic concentrations for which the PIE treatment fails.10J4J1J4 However, the treatment is essentially empirical in avoiding assumptions regarding values of a,and it is not obvious how the “best” values of the Langmuir parameters should be selected. The various pseudophase models have been applied largely to quantitative aspects of reactivity in micellar and similar colloidal systems in terms of reagent distributions between two distinct regions, e.g., the aqueous and micellar pseudophases.3~4JHowever, even if this problem is treated satisfactorily, we still have to relate second-order rate constants to ionic concentrations in the micellar pseudophase, which involves assumptions regarding the spatial distributions of both ionic and nonionic reagents a t the micellar s u r f a ~ e . The ~ - ~parameters ~~~ that describe these distributions depend on arbitrary assumptions, and there is no general agreement on the “best” values. Second-order rate constants have the dimensions of reciprocal time, and concentration is generally written as molarity. Thus estimation of second-order rate constants in micellar pseudophases depends on the dimensions of the reaction region at the micellar surface and spatial
+
Blask6 et al. distributions of reagents in the reaction region, as well as distributions between the pseudophases. Conclusions. The classical PIE model adequately describes competition between anions that have similar specific interactions with cationicmicelles. In these situations, LY (8)is approximately constant. Coulombic forces are assumed to be nonspecific, so micelle-ion interactions depend on individual ion specificities as described by the PIE model (eq 1). This approximation becomes less satisfactory as the ion-exchange parameter (eq 1) deviates from unity and a (8) changes as one ion replaces another. The PIE model seems to be unsatisfactory for competition between very hydrophilic anions whose interactions with micelles are largely Coulombic.19 Here the ion-exchange parameter (eq 1) should be close to unity. An increase of ionic concentrations decreases the micellar surface potential, which decreases concentrations adjacent to the surface. This decrease is more than offset by an increase in total ionic concentration,so concentrations in this surface region increase, which is equivalent to an increase in j3. Exchange models that allow j3 to increase with an increase in the total ionic concentration should be more sati~factory.1~J~ Equations of the Langmuir form with similar, low, ion-binding parameters might accommodate competition between ions that interact only Coulombically. The PBE model involves disposable parameters whose values are based on existing kinetic data.l5J* The reactions involved a variety of reactive anions, some of which are very hydrophilic, e.g., OH- with 6 0, but others, e.g., B r and C1-, interact specifically and require larger values of 6, but the same values of these parameters fit inhibition of reactionsof OH-, for example, by a range of anions, including B r and C1-. Thus both kinetic and NMR data are fitted with the same values of the disposable parameters. It appears that the PBE model fits data under some conditions in which the PIE model fails, but both models are reasonably satisfactory for mixtures of specifically-interacting ions.
Experimental Section Materials. Preparation and purification of the surfactants have been described.1” The solvent was H20:DzO 4:l v/v. N M R Spectroscopy. Line widths were measured on GN300 or 500 spectrometers as d e s ~ r i b e d . l Chemical ~ * ~ ~ shifts of 35Clwere referred to that with 0.05 M NaCl and no surfactant. Salts were added as concentrated solutions with a Hamilton syringe, and each set of measurements with a given salt were carried out within as short a time span as possible to limit errors due to instrumental drift. Each data point is the mean of three to five measurements. All experiments were a t 25.0 O C . Measurements with 0.05 M (CTA)Br were not treated quantitatively because of micellar growth and an increase in viscosity on addition of s a l t ~ . ~The ~ J results ~ are qualitatively useful because, even though NaOTos causes micellar growth and increases viscosity of (CTA)Br, in higher concentration it markedly decreases the line width of ’9Br. The line width of 7 9 B rin 4:1 H20:DzO v/v was measured with 0.02 M NaBr and Bw
