Polyelectrolyte-Induced Micelle Formation of Ionic Surfactants and

Aug 30, 1995 - The relation, which seems to be quite general, is very useful when the mixing ..... binary mixture of surfactants in a polyelectrolyte ...
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J. Phys. Chem. 1995,99, 16684-16693

16684

Polyelectrolyte-Induced Micelle Formation of Ionic Surfactants and Binary Surfactant Mixtures Studied by Time-Resolved Fluorescence Quenching Per Hansson*$tand Mats Almgren Department of Physical Chemistry, Uppsala University, P.O. Box 532, S-75121 Uppsala, Sweden Received: April 25, 1995; In Final Form: August 30, 1995@

A semiempirical model for the distribution of two cationic surfactants between subphases in solutions containing a polyelectrolyte of opposite charge is presented. The model, based on ideal mixing in the surfactant aggregates, is tested in fluorescence quenching experiments with satisfying results. An experimental relation which gives the critical aggregation concentration (cac) or critical micelle concentration (cmc) for dodecylpyridinium ions (C12P’) as a function of cac (or cmc) for dodecyltrimethylammonium ions ( C I ~ T A +under ) the same conditions is found. The relation, which seems to be quite general, is very useful when the mixing model is applied to results from fluorescence quenching. Binding isotherms for C,zTA+ in solutions of sodium polyacrylate (NaPA) at various concentrations of NaBr are reported together with estimated surfactant aggregation numbers. The aggregation numbers (60 f 4) are not affected by the presence of 0.01 m NaBr or by an increase in the polyelectrolyte concentration. The cac for C I ~ T A ’is found to increase both with increasing NaBr and NaPA concentrations, although stronger in the former case. We show that the interpretation of the polyion-surfactant interactions can be rationalized from an analogy with the self-assembly of free surfactant. From this perspective we estimate the “local cmc”, i.e. the critical concentration of surfactant close to the polyion when micelle formation starts. The local cmc is found to decrease with increasing salt and polyion concentration.

Introduction There are many similarities between the binding of ionic surfactants to polyelectrolytes of opposite charge and micelle formation of surfactants in water. In both cases, a cooperative aggregation of the surfactant starts in a narrow concentration range. The transition is sharp enough as to make it possible to characterize a system in part by its critical aggregation concentration (cac), or critical micelle concentration (cmc), a parameter which is rather easily obtained from experiments. It is customary to use the notation cac in the presence of polymers. It has been shown for homologous series of surfactants that ln(cac) decreases linearly with the number of carbon atoms in the surfactant tail, corresponding to a standard free energy change of 1.2 kT per CH2 group, i.e. close to what is found in free micelle formation.’X2 Furthermore, the cac shows a weak temperature dependence with a shallow minimum, resembling the temperature dependence of the cmc for free ionic surfact a n t ~ . Fluorescence ~,~ probing and quenching techniques indicate that the polyion-bound surfactants form discrete aggregates, with properties similar to free surfactant micelle^.^-^ The fact that the aggregation in solutions of highly charged polyelectrolytes apparently takes place without concomitant binding of the surfactant counterions partly explains the low cac generally found. It also suggests, and is supported by results from viscosity measurement^^.^ and photophysical studies,8 that the polyelectrolyte must change its conformation in order to maintain charge compensation. The cooperativity in the binding and the importance of entropic driving forces were pointed out early by Satake and Yang,” who investigated the interactions of anionic surfactants with cationic polypeptides. By attributing the cooperativity to a favorable interaction between bound surfactants, but otherwise neglecting the similarities with micelle formation, they derived a site-binding model based on the Zimm-Bragg theory for helix-coil transitions.I0 The model, which is similar to theories E-mail: [email protected].

’Abstract published in Advance ACS Abstracts, October 15, 1995

for the titration of polymers with strongly interacting takes into account nearest neighbor interactions between the surfactant tails and assumes that the electrical surface potential of the polymer is not affected by the binding. Strictly, this means that the bound surfactants cluster side by side along the polymer and replace equal amounts of polymer counterions. Although the model may not be physically realistic, it offers a possibility to quantify the interaction in terms of intrinsic binding constants and surfactant-surfactant interaction parameters. It has been widely usedi4to analyze data from binding studies, in order to identify important factors governing the interaction. The model makes no explicit use of micelles or aggregates, but an unbroken sequence of cooperatively bound surfactants can be regarded as a micelle, and an average aggregation number can be calculated and related to the strength of the cooperativity and the degree of binding. We and others3.l5 prefer to regard the binding as micelle formation electrostatically induced by the polyelectrolyte, which starts at a “local cmc”, i.e. when the concentration close to the polyelectrolyte-in the condensed layer according to Manning’s terminologyI6-exceeds a critical value. We shall discuss how the cooperativity parameter of Satake and Yang can be related, qualitatively, to the local cmc. We have also determined aggregation numbers with great care, with results showing that the dependence on salt, surfactant, and polyelectrolyte concentration is very different from the predictions of the cooperative site binding model. The determination of reliable aggregation numbers in polymersurfactant systems requires some consideration. Time-resolved fluorescence quenching is one of the few methods that can be used at low surfactant concentrations, but not without problems. One of these problems may appear trivial, but is often a stumbling block: there is always some impurity fluorescence in the system, and when very low probe concentration is used, the impurity fluorescence becomes particularly disturbing. We shall consider a method that has been used for some time in this laboratory to correct for such disturbances and show its reliability from test measurements.

0022-365419512099-16684$09.0010 0 1995 American Chemical Society

Polyelectrolyte-Induced Micelle Formation Another problem which emerges at low surfactant concentrations is that the fraction of unmicellized surfactant is important and difficult to assess exactly. The same is true for the quencher; even quite hydrophobic substances may have a nonnegligible fraction free in water at very low surfactant concentrations. Also the fluorescent probe could distribute between water and micelle. We have mainly used pyrene, however, which is very hydrophobic, to the extent that it sometimes presents another problem by associating with and stabilizing the few micelles that form before the proper cmc. In any case, it is usually possible to distinguish, in the measurements, between pyrene free in water and solubilized in micelles. The important problem, therefore, is the distribution of surfactant and quencher between micelles and water. Some time ago we realized that it would be advantageous to utilize a quencher that distributed in the same way as the surfactant between micelle and water. A useful quencher is the alkylpyridinium ion, which in itself is a cationic surfactant and can be expected to mix ideally in micelles with an alkyltrimethylammonium surfactant of the same alkyl chain length.7 In the first approximation we expected that quencher and surfactant would be present at the same ratio both in the micelles and in the aqueous solution. Even if the amount micellized is not known, the correct aggregation number can still be obtained from fluorescence quenching measurements. The method was introduced in a previous paper dealing with the interaction of alkyltrimethylammonium surfactants with anionic polyelectrolyte^.^ The free concentration of the surfactant was small compared to the concentration bound to the polyelectrolyte, and we could assume that the mole fraction of the two surfactants in the micelles was the same as the overall mole fraction (on a surfactant-only basis). This assumption is not valid when the concentration of free surfactant is large, since binding of the component with the lowest cmc will become increasingly favored. In the case of free micelle formation, given the composition of the surfactant mixture, the ideal mixing model allows the calculation of the mole fraction in micelles from the cmc values of the pure components. When the micelle formation is induced by a polyelectrolyte, one can expect it to be correct to use the cac values instead. To strengthen the basis and determine the application limits, we have considered the formation of mixed micelles in the polyelectrolyte solution.

Experimental Section Chemicals. Polyacrylic acid (Mw= 90 000, 25 wt % aqueous solution) from Aldrich; dodecyltrimethylammonium bromide (Cl2TAB) (analytic grade), and hexadecyltrimethylammonium bromide (cl6TAB) (crystalline pure), both from Serva, N-hexadecylpyridinium chloride (cl6Pc) from Merck, sodium bromide (analytic grade) from Bakers, pyrene (analytic grade) from Serva, and 3,4-dimethylbenzophenone(DMBP) from Aldrich were all used as supplied. N-Dodecylpyridinium chloride (C 12PC) from Aldrich was recrystallized several times from acetone. Sample Preparation. The concentration (as monomers) in an aqueous stock solution of polyacrylic acid was determined by titrating portions of it with a standard NaOH solution in the presence of 0.5 M NaBr. To prepare a typical mixture of surfactant, polyelectrolyte, and NaBr, the polyacrylic acid was first converted to sodium polyacrylate (NaPA) by adding to it an appropriate amount of NaOH. Then NaBr was added, and the solution was diluted with water and mixed. A small portion of surfactant stock solution (typically 0.02 m o m ) was added slowly under rigorous stirring. Finally, further additions of NaOH were made, if necessary, as to obtain pH =- 9. All samples were prepared by weighing. For samples used in the

J. Phys. Chem., Vol. 99, No. 45, 1995

16685

fluorescence measurements the surfactant stock solutions also contained pyrene (probe) or pyrene together with C I ~ P C(216, PC, or DMBP (quenchers). Pyrene and DMBP were dissolved in the surfactant stock solution in the following way. An appropriate volume of a solution of pyrene (or DMBP) in ethanol was added to a flask. The ethanol was evaporated with nitrogen, and the surfactant stock solution was added. The solution was stirred overnight. Electrode Measurements. Binding isotherms for Cl2TAB in aqueous solutions of NaPA were recorded potentiometrically with a surfactant sensitive membrane electrode at 25 “C. The electrode and the setup have been described elsewhere.6 In brief, a plastic membrane separates a reference solution from a test solution. On both sides a fraction of the surfactant, related to the activity, dissolves in the membrane and so gives rise to a measurable potential difference over the membrane. The test solution and the reference solution are, via agar salt bridges, connected to calomel electrodes placed in saturated potassium chloride solutions. Although the agar bridges are not in direct contact (compartmentsseparated by a pinhole) with the solutions in contact with the membrane, accumulation of salt in the samples, leaking from the agar bridges, can be a serious problem when recording isotherms in solutions containing low concentrations of extra salt (NaBr). To avoid that, separate solutions were prepared for each surfactant concentration tested. The concentration of free surfactant in a solution containing polyelectrolyte, NaBr, and surfactant was taken as equal to the concentration of a standard solution of the surfactant in 0.010 m NaBr giving rise to the same potential difference (see ref 7 for a discussion). Steady-State Fluorescence Measurements. Pyrene fluorescence spectra were recorded on a SPEX Fluorolog 1680 combined with SPEX DM3000 software. The slit widths at the detector side were 0.3 mm. Time-Resolved Fluorescence Measurements. The fluorescence decay data were collected at 25 “C with the single photon counting technique. A detailed description of the experimental technique and equipment is given el~ewhere.~ A problem often encountered in this type of measurements is the perturbation of the decays by fluorescence from impurities. Due to their short lifetimes, even trace amounts may give non-negligible contributions to the initial parts of the recorded curves. We suggested ear lie^ a way to handle this by adding to the function describing the decay a term representing the contribution from the impurity:

where F(t) represents the total decay, and Fp(t)describes the fluorescence from the probe according to the kinetic model of the system. Fe(t),the contribution from the impurity, can be described by

where w,is the fraction of the (estimated) total amplitude at zero time, F(O), from an impurity component with decay rate k,. Since the probe is usually much more long-lived than the impurities, proper wi and k, values can easily be obtained from a multiexponential fit of a sample containing no quencher. When fitting quenched experimental curves to eq 1, no extra parameters are used since Fp(0)= (1 - Z,w,)F(O). The correctness of this treatment was checked from measurements of the quenching of pyrene by Cl2PC in 0.044 m aqueous Cl2TAB solutions. Figure l a shows the decays from two samples, with and without 4.5 x low4m C I ~ P Cboth , containing 9 x m pyrene. Figure l b shows the result from the identical experiment, but with only 1 x lo-’ m pyrene. Here fluorescence from some impurity “always” present in surfactant samples has

Hansson and Almgren

16686 J. Phys. Chem., Vol. 99, No. 45, 1995

number of quenchers in a micelle, and kq and k- are the quenching rate constant and quencher escape constant, respectively, in a micelle. The weighted residuals from the fittings of the quenched curve in Figure l b is inserted into Figure IC, where the curves from Figure l b with the impurity fluorescence subtracted are shown. The results are summarized in Table 1. The aggregation numbers were calculated assuming ideal mixing of quencher and surfactant (see below). The compensation for the impurity is obviously satisfying. In general, we have used this type of treatment in the analysis of the data in this paper, although in all cases the contribution from the impurity was much smaller than shown in Figure lb.

i

1o2 0

50

100

150

200

250

300

350

400

t I ns

Ideal Mixing Model

I o5

I o4

io3

E 102

0

50

100

150

200 250 ns

300

350

400

250

300

350

400

t I

105

I o4

1o3

1o2

c

0

C

50

100

150

200

t I ns Figure 1. Pyrene fluorescence decays without (upper curves) and in m; (b) the presence of CtzPC (a = 0.0101): (a) [pyrene] = 9 x [pyrene] = 1 x lo-' m; (c) decays in b with impurity fluorescence subtracted. The inset shows the weighted residuals obtained from fitting the quenched curve to eq 1 with F,(t) (two extra exponents) and FJr) defined in eqs 2 and 3, respectively.

become evident due to the low concentration of the probe. The unquenched curve in Figure l b was fitted with three exponents, and the resulting two extra components were used in eq 1, where F,(t) is a function describing the quenching kinetics, of the form first proposed by Infelta et al.:I7 F&t) = A , exp[-A,t+A,{exp(-A,t)-l}l (3) Here A I = (1 - Ziwi)F(O). In the case of a stationary probe and a Poissonian distributed quencher that can migrate between micelles,1 8 A, = l/z0 kqk-(n)(kq k-)-'

+

+

+

A, = kq kl/zo is the natural fluorescence lifetime, (n) is the average

We derive here a semiempirical model for the distribution of surfactants between aqueous and micellar subphases in systems where ionic surfactants form mixed micelles in the field of a polyelectrolyte. The result can be used to calculate the mole fraction of the components in the mixed micelles if the data for the corresponding one-surfactant systems are available. The model is required to analyze the fluorescence quenching results with C,P+ as quencher in C,TA+ micelles, but is also of more general interest. We restrict the model to the case where the polyelectrolyte induces complexation of surfactants of opposite charge in dilute solutions; that is, the free concentration of surfactant is always below the cmc so that no free micelles exist. At concentrations below the cac a fraction of the surfactant ions and the simple counterions are assumed to be "condensed" on the polyelectrolyte. As the local concentration of surfactant in the condensed layer exceeds a critical value, micelles are formed. The equilibrium between bound surfactant monomers and surfactant in micelles will be approximated with a phase equilibrium, in complete analogy with the derivation by Clint for the case of free micelle f ~ r m a t i o n . 'For ~ the sake of simplicity, we consider all bound surfactants to have the same electrostatic potential Q, relative the bulk, where the potential is defined to be equal to 0. To summarize, free surfactant in the bulk is in equilibrium with surfactant bound in polyion domains at an electrostatic potential Q,. Within the polyion domain, monomers are in equilibrium with a micelle pseudophase. If we approximate the volume of the system to the volume of the bulk and let C? and c;' represent total and local surfactant concentrations, respectively, we can write the electrochemical potentials for micellized (x = m), condensed (x = c), and free surfactant (x = f) as

+

pim= pim,' RT In xi

+ Z~F@

(4)

ppo is the standard-state chemical potential, R is the ideal gas constant, and T the absolute temperature. X , is the mole fraction of i in micelles, and zIF is the charge of 1 mol of i . For simplicity, we assume that the ions in the bulk do not interact (see discussion below). In the one-surfactant system ( X I = l), eqs 4 and 5 together with the condition for phase equilibrium within the polyion domain, ,utm= p t c ,give p8m,o - plcXo = RT In c,C*

(7)

where c,C* is the local concentration of i in the condensed layer in the one-surfactant system. For the same phase equilibrium

J. Phys. Chem., Vol. 99, No. 45, 1995 16687

Polyelectrolyte-Induced Micelle Formation

TABLE 1: Results from Fluorescence Quenching Experiments and Calculations from the Ideal Mixing Model sample

[NaBr]/10-3m

quencher

NaPA-CIZTAB, p = 0.50

k,/107 s - l b

k-/105 s - l b

(@

118

3.4

2.9

0.68

0.0111

62d

1.13

118 207 212 215 217 21 1 227 222 227 228 23 1

3.1 2.1 2.0 2.1 2.2 2.5 1.9 1.8 1.9 2.0 2.2 1.9 1.8 2.0 1.9 2.2 1.7 1.5 1.7 1.8 2.0

2.7

0.67 0.70 0.80 0.90 1.1 1.5 1.5 1.4

0.01 11

61d 60 59 58 55 61 64 53 58 58 65

1.07 0.91 1.20 1.02 0.95 1.04 1.05 1.09 1.13 0.98 1.01 1.08 1.00 1.13 1.03 1.11 1.20 0.99 0.90 1.07 1.04

0 1.25 2.50 5.00 10.0

N~PA-CI~TAB, /3 = 0.66

0 1.25 2.50 5.00 10.0

N~PA-CI~TAB, i3 = 0.50

0 1.25 2.50 5.00 10.0

NaPA-CIZTAB, p = 0.66

x~~

rdnP

0.044 m C12TAB 9x m pyrene 0.044 m CIZTAB 1 x lo-' m pyrene

0 1.25 2.50 5.00 10.0

0.0 2.2 1.5 2.9 1.3 3.6 3.2 2.8 2.5 2.2

0.0 2.6 2.2 3.8 2.8 4.8 3.1 3.6 3.3 3.7

Xc

Xd

1.5 1.6 1.8 0.59 0.62 0.64 0.68 0.75 0.79 0.74 0.79 0.80 0.86

0.0098 0.010 0.011 0.012 0.012 0.012 0.014 0.013 0.014 0.013

0.0107 0.0113 0.01 19 0.0127 0.01 34 0.0140 0.0140 0.0140 0.0 140 0.0140

N~PA-CI~TAB, p = 0.50 1.04 10.0 3.9 3.4 0.20 2.4 x m DMBP 1.04 4.8 x m DMBP 10.0 4.0 3.3 0.42 1.21 10.0 3.6 3.4 0.77 7.6 x lO+'m DMBP 1.04 10.0 3.4 3.9 1.o 10 x m DMBP 0.30 m NaPA 2.5 4.9 0.79 0.0 120 66 0.94 2.5 x m C~ZTAB 210 0.0107 1.15 216 2.1 5.1 0.64 60 5.0 x 10-3m ClzTAB a Pyrene lifetime in equilibrium with air. Estimated in samples without quencher. Estimated from fits of eq 3 to quenched decays. Calculated from experimentally estimated ( n ) and N,,,. Calculated from ideal mixing model. e Quality of fit (quenched decays).fa= 0.010. we get the same expression as derived by Clint:

in the mixed system we can write RT In cf = pys0- p;,' -tRT In Xi which, together with eq 7, gives

(15)

with A' replacing A (=cmc2* - cmcl*) in his expression. Note that at the cac in the one-surfactant systems Cf* Cif* = caci*, and A' = cac2* - cacl*. For higher surfactant concentrations the full expression (14) must be used, since Cif* generally increases with increasing surfactant concentration. Clc* and C2c* are not easy to measure in any simple way. Estimations from the counterion condensationmodel (see below) or from a solution of the Poisson-Boltzmann equation, with the assumption that the surfactant concentrationin the condensed layer does not increase above the cac, show that it may be neglected at higher degrees of surfactant binding. Under those circumstances, the three-pseudo phase model is of course superfluous, and Clint's equation can be used directly with A = C2f*- Clf*. Application to TRFQ. In this and the following paragraphs we drop the subscripts on X and a and use them only with reference to the quencher. The measurements give (a) = XNass (see below), and it is clear that with A', C, and a known, X can be calculated and Nags obtained. From eq 14 we find that as long as C >> A', and then also (C/A' - 1 ) >> X , X = a holds.

+

(9)

c; = XiCf*

From the equilibrium with the bulk (pic= pif ) we obtain RT In Cif = pf" - pif.'

X I 2- (1 - C/A')X, - a,C/A' = 0

(8)

+ RT In c; + z,F@

(10)

By choosing picso= pFo and substituting from (9) for cf,

where Cif* is the equilibrium concentration of i in the bulk for the one-surfactant system. The last equality is justified if the electrostatic interaction of i with the polyelectrolyte is the same in pure and mixed systems (0= @*). As expected, cfIcic* = Cif/Cif*, with this assumption. Defining ai as the fraction of component i of the total surfactant concentration, C, gives

Results and, in the case of two surfactants (1 and 2),

X,= [a,C - (c,'+ C,~>]/[C- (cIc + elf) - (c;

+ c,~)I (13)

Finally, by noting that from (9) and (1 1) C: Cif*)X; and the definition

A' = (C2'*

+ C?)

+

+ Cif = (C:* +

- (CIc* CIf*)

(14)

Binding Isotherms. The binding of C I 2TAB to NaPA (fully ionized, monomer concentration 0.50 x m),in aqueous solutions containing different amounts of NaBr, was investigated by activity measurements using a surfactant sensitive electrode. Experimental curves are given in Figure 2, where the calibration curve, on a logarithmic concentration scale, is seen to be linear with a slope close to Nernstian (57 mV/decade). Binding isotherms, constructed as described in the Experimental Section,

Hansson and Almgren

16688 J. Phys. Chem., Vol. 99, No. 45, 1995 I20

I " '

0.85

" "

100

,

1

0,80

80 0.75

60 i

40

\

m

0.70

20 0.65

0 0.60 0.55

J 10 10

[C12TAB]/ molal

0,85

b

.

0,8

.

n

. . m

0,80

-

0.75

-

0,70

-

0.65

-

0,60

-

i-(

10.~

10.'

[ C,,TAB] I molal

Figure 3. Binding isotherms constructed from data in Figure 2. p, the (apparent) fraction of polyion charges neutralized by surfactant, is presented as a function of the equilibrium free concentration of

surfactant (symbols as in Figure 2). Lines show the results from fittings to a normalized version of eq 28 (see text). u = 60, 211, 207, 349, and 875 (from left to right).

-d

P

10.'

\

3

lo.A

o-s m4

1

to3

([NaPA]

+

to2 [NaBrl) I molal

lo"

Figure 4. Dependence of cac for COTAB on the sodium ion m NaPA and 0, concentration in solutions containing (0)5.0 x 1.25, 2.50, 5.00, and 10.0 x m NaBr (estimated in Figure 2); ( 0 ) 0.10, 0.50, 2.0, 5.0, and 15 x m NaPA (estimated in Figure 5). Dependence of cmc for C12TAB on NaBr concentration is also shown (A). The cmc in pure CUTABis indicated by an arrow. Data are from Jones and P i e r ~ y . ~ ~

are shown in Figure 3, The degree of binding, /3, is expressed as the number of bound surfactants per monomer of the polyelectrolyte. The isotherm corresponding to 0.010 m NaBr agrees very well with that reported by Hayakawa et. al. in the presence of 0.010 m NaCl.*O The sharp rise in /? at a certain surfactant concentration (cac) indicates the onset of cooperative binding. The cac is shifted toward higher surfactant concentrations with the addition of salt, as shown in Figure 4. Compare with the effect of salt in polyelectrolyte-free solutions. This phenomenon is well described in the literature2' and can be explained by the statistical distribution of the surfactant ions and the polyelectrolyte counterions.' The effect of salt is larger

10'~

[CI,TAB] / molal

Figure 5. Ratio of the third and first vibronic peak in the pyrene fluorescence spectra obtained in solutions of CI~TABand NaPA. [pyrene] = 1.5 x lo-' m. (a) 0.10 (+), 2.0 (O), 15 (m);(b) 0.50 (e), 5.0 (0) x m NaPA.

here than in systems where there is an additional hydrophobic interaction between the polyelectrolyte and the surfactant.22The cac values in Figure 4 were estimated from Figure 2 as the surfactant concentrations corresponding to the first break points in the emf curves. The cooperativity in the binding decreases abruptly at p E 0.6, reflecting the satpration of the polyelectrolyte. As a consequence, the binding isotherms for the different salt concentrations will approach each other at high free surfactant concentration. In Figure 3, the isotherms, except the one for the salt free case, intersect at /? E 0.66, corresponding to a free concentration of 0.55 x m (total concentration: 0.88 x m). In this region, the calculated value of /3 is very uncertain. Even a small error in the experimental data will give a large error in p. Effect of NaPA Concentration on cac. The sensitivity of the vibronic peaks in the fluorescence spectra of pyrene to the polarity of the environment was used to probe the cac for C12TAB in aqueous solutions of NaPA. The ratio between the third and the first peak (3/1) as a function of surfactant concentration is given in Figure 5. Each point is the average from two or three measurements on the same sample. The concentration of pyrene was kept as low as possible to minimize its influence on the micellization. In Figure 4,the estimated cac values are given as a function of the concentration of NaPA. Each cac was taken as the concentration of surfactant where the lines in Figure 5 intersect. The relation is close to linear on a log-log representation. This was observed earlier for sodium poly(styrenesulfonate).' A comparison between the cac obtained by the 311 method and from electrode measurements (Figure 2 ) is possible in the case of 0.5 x m NaPA with no salt, where we have data

J. Phys. Chem., Vol. 99, No. 45, 1995 16689

Polyelectrolyte-Induced Micelle Formation I.'

.>

.

r.1

' I

/

/

0'018

i

e

I X

-5

-45

-4 - 3 S -3 -2 5 log cac(C,,TA' / molal)

-2

-1 5

Figure 6. Logarithm of cac and cmc for C I ~ P given + as a function of the corresponding value for C12TA+ in various environments. Data from the literature. ( 0 )5 x m sodium dextran sulfate, 0.005-0.1 m NaC1;2.22(0):5 x m sodium alignate, 0.01 m NaC1;23.25(W) 5 x m NaPA, 0.01 m NaC1;23.25(0)0.5 m NaBr;' (A)pure C12PB/ C12TAB; (A) pure C I ~ P C / C I ~ T ALine C . ~represents ~ a least squares fit to the data.

from both methods. It is obvious from Figure 4 that the increase in the 3/1 ratio starts at a lower surfactant concentration than what is reported by the emf data. This is expected since pyrene can solubilize in and even stabilize micelles formed before the cac. The 311 ratio is also increased due to the high quantum yield for pyrene in micelles compared to pyrene in water. Distribution of C12P+. Test of Model. Equation 15 gives the mole fraction in micelles for one of the components in a binary mixture of surfactants in a polyelectrolyte solution. The validity of it was tested by introducing small amounts of C12PC (a 0.01) in the systems of ClzTAB/NaPA/NaBr used in the binding study. To calculate the mole fraction of C12P+ in the micelles, we needed to know the free concentration of surfactant, or strictly C?* 4-C,f*,for the one-surfactant systems corresponding to the mixed systems. A good approximation here is to neglect the small fraction in the condensed layer, C[*, if the total concentration of surfactant is well above the cac or, equivalently, if /3 is large. Binding data is available both for ClzP+ and for C12TAf in 0.5 x m solutions of NaPA with 0.01 m NaC1. However, a more general relation between the free concentrations of C12P+ and C I ~ T Ais + presented in Figure 6, where we have used cac and cmc data for various polyelectrolyte and polyelectrolyte-free solutions reported in the literature. Each point relates the log(cac) or log(cmc) for the two surfactants in the same environment. All data are for sodium salts of the polyions andor NaBr/Cl. A least-squares fit gives

+

log[cac(CI2P+)/m] = 1.08 1og[cac(Cl2TA+)/m] 0.0159

(16) Note that the point for the present system lies on the fitted curve. Since the concentration of Cl2PC is very small compared to Cl2TAB in our experiments, the mixed cac and the free concentration of C12TAB in equilibrium with bound surfactant are in practice not affected by the presence of C I ~ P C .Thus, for each surfactant/NaPA/NaBr mixture, Cif* for C12TAf was taken directly from the binding isotherm. With support from the apparent generality in Figure 6, Cf* for C12P+ was calculated from eq 16; see the Discussion section. Finally, the difference A' to be used in eq 15 was calculated. Two series of tests were made. For each salt concentration used in the binding study (0, 1.25, 2.5, 5.0, and 10 x m NaBr), C12TAB concentrations were chosen to correspond to p = 0.50 and p = 0.66. Note that at p = 0.66 the total concentration of surfactant is approximately the same for all salt concentrations (except zero salt). The results from calculations of the mole fractions of Cl2P+ in micelles from eq 15 are

0

2

4 6 [NaBr] / lo3 molal

8

10

Figure 7. Theoretical (open symbols) and experimental estimations of the mole fraction of C12P+ (a = 0.0101) in mixed micelles with m solutions of NaPA, at various C12TA+ formed in 5 x concentrations of NaBr. Circles: p = 0.66 (0.7 for zero salt). Squares: /3 = 0.50.

given in Table 1. The composition of the micelles was then estimated experimentally, taking advantage of the pyridinium ions ability to quench the fluorescence from pyrene (dissolved in the micelles). The following relation was used for the mole fraction of C12P+ in micelles:

where (n) is the estimated number of quenchers (C12P+ ) per micelle and Nasgis the micellar aggregation number (including the quencher). Nagswas estimated in separate experiments with c16Pc replacing ClzPC as quencher (see below). The results are presented in Figure 7. Distribution of DMBP. The distribution of the nonionic substance DMBP (a common quencher in aggregation number estimations) between aqueous and micellar subphases was determined in solutions containing 0.50 x m NaPA, 0.65 m NaBr Cp = 0.50). From x m C I ~ T A Band , 10 x fluorescence measurements, using DMBP as quencher, ( n ) was estimated for a series of DMBP concentrations. Since the concentration of surfactant and quencher in micelles, [SI, and [ Q l m , respectively, are related by

the distribution constant, KD,defined as23 KD

= [QI,~([Sl,~Ql~)

(19)

may be calculated with the knowledge of Nags and the total quencher concentration. [Qlf is the free concentration of quencher. We obtain from the data given in Table 1 KD = 2.7 x lo3 M-I, as an average from the different samples. To relate this value to the solubility in free micelles, KD for DMBP in pure C12TAB solutions was estimated from absorption measurements on DMBP-saturated solutions with a technique described elsewheree6 A least-squares fit of [Qlm as a function of [SI, gave KD = 2.8 x lo3 M-I. [Q]f was estimated as 6.5 x M in the saturated solution, and the free concentration of C12TAB was taken as 14.2 mM.24 Aggregation Numbers. Effect of Salt. The Aggregation number for C I ~ T A Bin 0.50 x m aqueous solutions of NaPA containing 0-0.01 m of NaBr was estimated with c16PC as quencher. Since the cac for Cl6Pc is more than 2 orders of magnitude lower than for C I ~ T A Bwe , assumed that there was no free cl6Pc. The results are given in Figure 8. Neither at C I ~ T A Bconcentrations corresponding to /3 = 0.50, where the binding is cooperative, nor at /3 = 0.66, where the binding is noncooperative, is there any pronounced effect of salt on the aggregation numbers. Remember that for p = 0.50 the free concentration of surfactant increases with the concentration of added salt, while for p = 0.66 the concentration of free and

16690 J. Phys. Chem., Vol. 99, No. 45, 1995 80

70 75

45

Hansson and Almgren

t

1 b

40 0

2

4 h [NaBr] / lo'' molal

8

10

m NaPA, Figure 8. Aggregation number for C12TA' in 5 x determined with CI6PCas quencher, in the presence of NaBr. Symbols as in Figure 7.

bound surfactant is approximately constant. The estimated value of the aggregation number, taking the average over all samples, is 60 f 4. Effect of Polyelectrolyte Concentration. The aggregation number for C I ~ T A B in a 0.3 m solutions of NaPA was estimated with CIZPCas quencher. The mole fraction of quencher in the micelles was calculated from the ideal mixing model, using 1 x m as the free concentration of C I ~ T A B ? The results for two C12TAB concentrations, 2.5 x and 5.0 x m, are given in Table 1. This corresponds to very low degrees of binding Cp < 0.01). At higher surfactant concentrations the system phase separates asso~iatively.~,~ The aggregation numbers are about the same as in the dilute solutions. Note that, since we do not know the exact concentration of C12TAB in the micelles, C12PC is preferred over c16Pc as a quencher here. This is due to the fact that it distributes similar to C12TAB between the subphases; see the Discussion section.

Discussion Ideal Mixing Model. Not surprisingly, the simple model derived for the mixing of two surfactants in micelles formed in the field of a polyelectrolyte is not in perfect agreement with experiments; see Figure 7. Remember, however, that the theoretical points are calculated solely from C, a, and A'. When the concentration of bound surfactant is fixed at 2.5 x m Cp = O S ) , the free concentration increases from 6.3 x to 4.0 x lop4 m as the added salt goes from 0 to 0.010 m. Consequently, the mole fraction in micelles of the more hydrophobic surfactant should increase with increasing free concentration of surfactant. At least qualitatively, the model is able to predict this behavior. The expression for the chemical potential of the surfactant in the bulk phase assumes ideality. This is not expected to introduce any errors in the model since the surfactant will deviate to the same extent in the one-component system as in the mixed system; any activity coefficients introduced will cancel out in eq 11. This is the advantage of the semiempirical approach. Likewise, the absence of an activity coefficient in eq 5 will only neglect the ClzP+-C12TA+ interactions in the condensed layer, not the self-correlation of the surfactant or the interaction with sodium ions. In fact, ideal mixing in the micelles implies an ideal mixing of C12P+ and C,2TA+ (with respect to each other) in the condensed layer as well. The assumption of pseudophases with different electrostatic potentials is expected to introduce errors. It is important to realize, however, that even though only two levels in the electrostatic potential are defined in the model, there are electrostatic contributions to the free energy included in the standard chemical potentials. Clearly, the final relations are

still obtained if the ziF@ terms are included in the standard chemical potentials, with the condition that u,O.; t plfxo. The reason for using a separate electrostatic term is just to underline the importance of the polyion. From another point of view, the analogy with a phase separation (a completely cooperative process) is not obvious for the equilibrium between monomers and micelles in polyelectrolyte solutions. Even if the cac is distinct, the free surfactant concentration, and therefore the chemical potential of the surfactant, may increase rather rapidly above the cac. This is in rather sharp contrast to a phase separation, where the chemical potentials in the phases do not change. In Figure 7 we have included results from experiments where the free surfactant concentration is well above the cac f$ x 0.66). The binding in this region is not at all cooperative (see Figure 3); still the theoretical predictions agree with experiment to the same extent as when the binding is cooperative. This result is important since it implies that aggregation numbers can be estimated even in systems where the free concentration and the concentration of surfactant in micelles is not accurately known. As an example, we can consider the NaPA-Cl2TAB system in the presence of 0.01 m NaBr in this study, mixed to contain 0.88 mM surfactant. Imagine that the cac is estimated to 0.3 mM, but no binding isotherm is at hand. From this we can only state that the concentration of ClzTA+ in micelles is less than 0.58 mM and that the free concentration is between 0.3 and 0.88 mM. Now, if (n) = 0.85 (Table 1) is obtained from experiments with CIZP+as quencher (a= 0.01), we can conclude from the ideal mixing model and eq 16 that 50 < Nagg < 70. In contrast, with a quencher that is exclusively distributed in the micelles (e.g. c16Pc) we can only state that Nags < 114 (as calculated from the estimated concentration of aggregates). With the further reasonable assumption that the concentration of C I ~ T A in + micelles is in the range 0.25-0.5 mM (that is, 0.5 < /? < l), we may conclude that 56 < Nagg< 70 and 49 < Nagg < 98 in the former and the latter case, respectively. Thus, from the mere fact that we know the mutual distribution of Cj2TA+ and C12P+ in the system, we can rather accurately estimate the aggregation number without a detailed knowledge of the binding. The almost constant difference between experiment and theory in Figure 7 suggests errors of systematic nature. This could be an indication of deviations from ideal mixing in the micelles. The issue is complex, however, as deviations from ideal mixing would affect not only the distribution between the aqueous and micellar subphases but also the distribution of the quenchers over the micelles. In the TRFQ measurements, a Poisson distribution is assumed, which at low (n) would be a good approximation to the binomial distribution that should be characteristic for two ideally mixed surfactants. The distributions resulting from an effective interaction between the quenchers have been discussed by Bales and Stenland.26 An effective attraction between the quenchers implies that there are more micelles without quenchers than according to the Poisson distribution, which means that the TRFQ method would underestimate (n) and with that the aggregation number. The deviation would disappear on extrapolation to zero quencher concentration. The discrepancies in Figure 7 can, thus, be due to errors in both the theoretically and experimentally obtained X values. Interestingly, recent results f r o n ~estimations of mixed cmc's made in our laboratory indicate that there is a weak effective attraction between Cl2PC molecules in mixed micelles of ClzPC and C I ~ T A C This . ~ ~ is consistent with an underestimation of X from experiments with ClzPC as quencher, if the aggregation number estimated with c16Pc as quencher is assumed to be correct. Due to packing problems, the attraction between Cl6p+ molecules in C I ~ T Amicelles + is in fact expected

J. Phys. Chem., Vol. 99,No. 45, 1995 16691

Polyelectrolyte-Induced Micelle Formation to be weaker than between Cl2P+ molecules, or even repulsive. This would further contribute to an underestimation of the experimental X values. Furthermore, an effective attractive interaction between C12P+ in the micelles implies an activity factor larger than 1 of C12P+ in the mixed micelles. If we consider the effect from that on the distribution between aqueous and micelle subphases, the assumption of ideal mixing would overestimate the theoretical X values. In conclusion, deviations from ideal mixing will affect both the distribution of C I ~ P + between micelle and aqueous subphases and the distribution of CI~P+ over the micelles. Both effects will contribute in the same direction, as to make X values estimated from the ideal mixing model larger than the experimental values in the case of an effective attraction between C I ~ P +ions in the mixed micelles. Micelle Formation in the Field of a Polyelectrolyte. In systems where the polyelectrolyte contains hydrophobic moieties the interaction with surfactant is stronger, and the effect of salt on the cac is smaller22 than for hydrophilic polyelectrolytes. This indicates that there is a hydrophobic interaction not only between the surfactants but also between the surfactant and the polymer. When C12TA+ ions aggregate in solutions of sodium poly(styrenesulfonate), hydrophobic parts of the polyelectrolyte are evidently taking part in the micellar structure.28 On the other hand, with a hydrophilic polyelectrolyte the interaction with the surfactant is expected to be mainly electr~static,~ although the chemical nature of the charged groups is expected to be important in some cases.29 The interaction is still very favorable; with the polyelectrolyte reducing the repulsion between the surfactant head groups, micelles can be formed without the great loss in entropy from the ordering of surfactant counterions. The cac for a given surfactant should then be determined by the interplay of parameters such as charge density and flexibility of the polyion and the concentration of polyion and simple salt (if present). Clearly, with a short persistence length it will be simpler for the polyion to reduce the surface potential of the micelles. On the other hand, the more flexible a polymer is, the more configurational entropy it will lose when binding to micelles. Aggregation of C12TA+ and C12P+. For the aggregation of two different surfactants in identical surroundings, the cac (or cmc) values give information about the difference in hydrophobicity (or surface activity) and in interactions with counterions, etc. The relation between the cac (cmc) values for C12TAf and C12P+ given in Figure 6 is therefore interesting. Inasmuch as the difference in interaction free energy between a surfactant ion i in a micelle and in the bulk can be expressed as Apo(i) = kT In cat;

(20)

eq 16 gives

+

Ap0(C,,Pf) = 1.08 APO(C,~TA+) 0.037kT

(21)

where k is the Boltzmann constant. Clearly, the drastic environmental differences behind the data in Figure 6 affect the nature of the micelles of the two surfactants in a surprisingly similar way. However, the fact that the difference Ap0(Cl2P+) - b0(Cl2TA+) is not constant (the slope is not unity) but changes from about -0.82kT to -0.25kT in Figure 6 shows that the aggregation of Cl*P+ compared to C,2TA+ becomes increasingly more favorable as the cac values decrease. The generality of the effect shows, however, that it is not due to the replacement of simple counterions with a polyion as such. It could reflect a difference between the two surfactants in the way the relative strengths of steric and electrostatic repulsions respond to environmental changes. Due to the influence of

electrostatic interactions on the effective surfactant head group area in the micelles, it is expected that the difference in cac (or cmc) is smallest when the electrostatics is most important. While this can explain the behavior in the polyelectrolyte-free solutions, it is not straightforward to use the same argument when the micelle formation is induced by the polyelectrolyte. In this case, it is important how changes in the bulk electrolyte concentration affect the polyelectrolyte in general and particularly how the local interactions close to the polyion, where the micellization takes place, are affected. Local cmc. Cac values for C12TAB in different solutions containing NaPA are given in Figure 4. We see that the effects of adding NaBr and NaPA are related. This can be further investigated by a calculation of the average concentration of surfactant in a small volume surrounding the polyelectrolyte when total surfactant concentration is equal to the cac. We emphasize that the purpose of the calculation is not to correctly estimate but to illustrate how the surfactant concentration close to the polyion changes when NaBr or more polyelectrolyte is introduced. We are interested in the local concentration at the cac, i.e. a "local cmc", which we shall call Pat. If we assume that the surfactant and the sodium ions are distributed in the same way at concentrations below cac, a rough estimate of c ~ can be obtained from the simplest version of the counterion condensation model,I5 based on the postulate that a constant fraction, P,,,, of the polyion charges are neutralized by counterions in the limit of infinite dilution. For univalent counterions, independent of the concentration of salt in the system,

p'"'

= 1 - 116

E = e2/(4mkTb) (23) where 6 is the polyion linear charge density parameter, e is the proton charge, E is the bulk permittivity, k is Boltzmann's constant, and b is the average linear charge separation on the polyion backbone. At the cac, the average concentration of surfactant in a cylindrical shell of inner radius r, outer radius R, and length b surrounding the polyion is evaluated as Cc.cac -

- 8pto'/(N,bn(R2 - r2})

(24)

where

8 = cac/(cac

+ CNaBr+ CNaPa)

(25)

C N ~and B ~C N ~are A total concentrations of NaBr and NaPA, respectively. Na is Avogadro's constant, and r is the radius of the polyion. The result from calculations with data from Figure 4, with R = 20 A (chosen to correspond to the radius of a micelle), r = 3 A, b = 2.5 A, and 6 = 2.85, is presented in Figure 9. c ~is given . ~as a~function ~ of the total concentration of sodium ions in solutions containing (1) 0.1 x to 15 x m NaPA and (2) 0.5 x m NaPA and 0 to 10 x m NaBr. Despite the increase in cac, the local cmc (which is proportional to the "critical degree of binding"7) decreases as electrolyte is added. While the effect is small when NaBr is added, increasing the NaPA concentration seems to facilitate the aggregation of bound surfactants. Even though the calculation is very approximate, it suggests that the local cmc values are on the same order of magnitude as the normal cmc. Since the clustering of bound surfactants can occur without the binding of the surfactant counterions, this local cmc must be considered as high, probably reflecting the difficulties of the polyelectrolyte to compensate for the charges on the micelles. It is very interesting that, while the cac increases, both the local cmc and the cmc in polyelectrolytefree solutions decrease when salt is added. A possible explanation is that by the addition of salt the electrostatic screening

,

~

~

Hansson and Almgren

16692 J. Phys. Chem., Vol. 99, No. 45, 1995 makes the polyion more flexible, and by that, the aggregation of bound surfactant is facilitated (decrease in local cmc). At the same time, a higher bulk concentration of surfactant is required to obtain the same local concentration close to the polyion (increase in cac). We may also slightly digress to note that /3 (=@YOt), at the cac, changes from about 0.08 to 0.01. A typical value of 0.02 gives an average distance of 125 A, along the chain, between two bound surfactants. Finally, it is important to keep in mind that the simple counterion condensation model lacks a rigorous theoretical basis. Furthermore, the way we have used it is principally not correct, since the model does not give any information about the distribution of ions close to the polyion. However, more rigorous models and experimental results show that the effect of salt and polyion concentration on the counterion concentration close to a polyion is rather small within reasonable concentration limits.’O The Cooperatiuity Parameter. In the literature, the aggregation of ionic surfactants in solutions of polyelectrolytes of opposite charge has been modeled either as a site binding of interacting ligands to the or as a micelle formation electrostatically induced by the polyele~trolyte.~,’~ The local cmc used in this paper derives from the latter perspective. It is illuminating, however, to see that there is a counterpart in the former case, where free surfactant molecules react with sites on the polyion. The sites are arranged in a one-dimensional lattice, and the interaction between surfactants is restricted to nearest neighbors. The surfactant-surfactant interaction parameter, u, often referred to as the “cooperativity parameter”, can be thought of as the equilibrium constant for the “reaction” between pairs of sites (symbolized by parentheses):

+

2(01) = (00) (1 1) (26) where “0” and “1” represent unoccupied and occupied sites, respectively. Thus, we can write for the standard free energy change in 26

+

AP’ = w , ~ woo - 2w0, = -kTln(u)

(27) where W I Iwoo, , and w01 are the interaction free energies for the pairs of sites defined by 26. In terms of micelle formation in the field of the polyelectrolyte, kT 1n(Pac) is the change in free energy in the process of transferring an isolated bound surfactant into an aggregate. Clearly, (cc.cac)-Iis conceptually related to u. The binding isotherm obtained from the model is given by

/3 = { 1

+ ( K u d - l)/[(l - KuC‘)’ + 4KCf]”2}/2

(28) where K is the constant for the binding of free monomers to isolated sites. Note that Ku can be interpreted as the constant for the binding of a free monomer to a site adjacent to an occupied site, Le. the cooperative binding constant. For the special case of /3 = 1/2, eq 28 reduces to d = (Ku)-’. Thus, for a highly cooperative binding, which results in steep isotherms, (&)-I cac. In applications of eq 28 in the literature, /3 has been taken as equal to the fraction of polyion charges neutralized by surfactant. As K is independent of @, the model is only meaningful as long as K is unchanged. The most obvious criteria that must be fulfilled is that the binding of surfactants should be accompanied by a release of an equivalent amount of “condensed” counterions, as to maintain a constant surface potential. Now, the fraction of polyion charges “neutralized” by counterions is always less than unity, which implies that the concentration of sites available for the type of binding accounted for in the model is smaller than the concentration of polyion charges. Thus, in our opinion, a more correct estimate of the binding parameters K and u is obtained if p in eq 28 is normalized to the level of

€

n

. 5

Y

U

25 20

I b 1

0

2

4 ([NaPA]

+

6 8 1 0 1 2 1 4 [NaBr]) / l o 3 molal

Figure 9. Local cmc, Pat, calculated from eq 24 corresponding to cac values in Figure 4 (same symbols) and l / u from the fitted curves in Figure 3 (0).

saturation in the isotherms. The type of binding generally observed at higher surfactant concentrations is not accounted for in the model. A normalized eq 28 was fitted with two parameters to the data in Figure 3. The estimated u values changed from 60 to 875 when going from the salt-free case to 0.010 m of NaBr. The normalization was introduced by multiplying the right-hand side of eq 28 by the experimentally obtained /3 at the first level of saturation in the experimental isotherms. The choice of this saturation level is somewhat arbitrary and not the same for all salt concentrations; however, the fittings were not so sensitive to small variations. The u parameters were inverted and multiplied by 1 M to obtain the corresponding local cmc values (cc.cac). These are indicated in Figure 9. The agreement with the values calculated from the condensation model is rather poor. It must be emphasized, however, that the estimations of u from the binding data are rather uncertain. Furthermore, due to the unrealistic assumptions in the model, K and u are not true constants, and therefore, the meaning of the estimated u becomes obscure. On the other hand, the values calculated from the condensation model are probably overestimated since the smaller sodium ions will be distributed closer to the polyelectrolyte than the surfactant. The error is expected to be larger the more salt present. Aggregation Numbers. The aggregation numbers reported in Figure 8 are comparable to those of free micelles of C12TAB/C. The values are slightly smaller than reported in a previous study,’ where we assumed that C12TA+ and C12Pf were distributed identically between micelles and water. Although the addition of 0.01 m NaBr changes the cac dramatically, the effect on the aggregation number is small. This is expected, since the addition of salt is not big enough to considerably affect the electric double layer. Interestingly, the aggregation number found in 0.3 m solutions of NaPA is about the same as in the dilute solutions; see Table 1. This indicates that, as long as the micelle formation can be considered as induced by the polyelectrolyte (thus, not only a general salt effect), polyacrylate has no possibility to influence the packing conditions so as to allow for a growth of the micelles. The value is in approximate agreement with a recently reported aggregation number34 (Nagg = 49, 57) for 3 mM C12TAC in 0.1 M solutions of NaPA.2S The cooperative binding model discussed above also gives an expression for the average aggregation number or, rather, the average length of unbroken surfactant sequences in the lattice; see eq 21 in ref 10. The aggregation number is a function of both /3 and u and is predicted to increase with both. For p = 0.5, Nagg% u1I2is a good approximation. Accordingly, to obtain an aggregation number of 60, u must be equal to 3600 (local cmc x 0.3 mM), a value much larger than reported for C I ~ T A Btogether with any polyelectrolyte. The values of u

J. Phys. Chem., Vol. 99, No. 45, I995 16693

Polyelectrolyte-Induced Micelle Formation obtained from the binding isotherms in Figure 3 would correspond to an increase in the aggregation number at /3 = 0.5 from 9 to 31, when going from the salt-free case to 0.010 m of NaBr. No such trend is observed in Figure 8. In a previous paper we showed that the aggregation numbers for C I ~ T A Band Cl6TAB micelles formed in complexes with sodium poly(styrenesu1fonate) did not change with p. The results obtained in this study for ,8 < 0.01, p = 0.5, and p = 0.66 likewise suggest that the aggregation numbers are rather insensitive to p. The fact that the aggregates formed are threedimensional, with an optimal size, can probably explain many failures in the predictions from the cooperative binding model. Solubility of DMBP. The aggregation number for C12TAf and the mixing of C12P+ and C12TA+ in the aggregates formed with NaPA reveal great similarities to the nature of free C12TABK micelles. The solubility of DMBP in the NaPA-Cl2TAB micelles, a parameter expected to be sensitive to the aggregate microstructure, gives further support to this. The distribution constant (KO= 2.7 x lo3M-I) is close to the value found in aqueous solutions of C12TAB (2.8 x lo3 M-I) and sodium dodecyl sulfate (2.6 x lo3 M-I) at 25 0C.35 These values can be compared to those found in sodium poly(styrenesulfonate)-CI2TAB (5.7 x 10’ M-1)6and CI~TAC/HZO (5.4 x lo3 M-1),35where in the former case the aggregation number was reduced roughly by a factor of 2 from the free micelle values.

Conclusions Two important results for the method of fluorescence quenching are found. First, recorded decays from fluorescence quenching experiments, perturbed by fluorescent impurities, can successfully be analyzed by the introduction of an extra term describing the decay law of the impurity to the fitting function. Second, the distribution of the quencher C12P+ between aqueous bulk and micelles formed by C I ~ T A +in the field of a NaPA can be well described by a model based on ideal mixing. For Cl2TA+ in solutions of NaPA we can confirm the wellknown fact that the cac in polyelectrolyte solutions increases with additions of simple salt. We can also conclude that the cac increases with the NaPA concentration in salt-free solutions. The effect of simple salt is somewhat stronger than the effect of polyion concentration. On the other hand, approximate calculations of the local concentrations of surfactant close to the polyion at concentrations equal to the cac suggest that the “local cmc” decreases slowly with the bulk concentration of NaBr, but faster with increasing NaPA concentration. The aggregation number for the Cl2TA’ micelles formed is not affected by the changes in salt concentration (0- 10 mM NaBr) or by changes in NaPA concentration. The estimated aggregation number 60 is approximately the same as in 0.044 m C12TAB (62). Thus, it seems like the NaPA can offer an environment that is favorable for the aggregation of C I ~ T A + into micelles with properties similar to free micelles of the same surfactant. This is supported also by the fact that DMBP can be solubilized equally well in polyion-bound micelles as in the free ones and that the mixing of CIZTA+and CIZP+in the micelles is similar in both cases. The “cooperativity parameter” in the site-binding model by Satake and Yang is conceptually related to the local cmc. However, the strong similarities between free micelle formation

and polyelectrolyte-induced aggregation found here points to the importance of the surfactant molecular geometry for the understanding of the aggregationhinding. This is not considered in the Satake-Yang model.

Acknowledgment. We are grateful to Mr. Goran Karlsson for skillful preparation of the electrodes. This work was supported by grants from the Swedish National Board for Industrial and Technical Development (NUTEK). References and Notes (1) Malovikova, A,; Hayakawa, K.; Kwak, J. C. T. In Structure/ Performance Relationships in Surfactants, 2nd ed.; Rosen, M. J., Ed.; American Chemical Society: Washington, DC, 1984. (2) Malovikova, A,; Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1984, 88, 1930-33. (3) Skerjanc, J.; Kogej, K.; Vesnaver, G. J. Phys. Chem. 1988, 92, 6382-5. (4) Santerre, J. P.; Hayakawa, K.; Kwak, J. C. T. Colloids. Sur$ 1985, I S , 35-45. (5) Abuin, E. B.; Scaiano, J. C. J. Am. Chem. SOC.1984, 106, 627483. (6) Almeren. M.: Hansson, P.: Mukhtar, E.: van Stam. J. Lannmuir 1992, 8, 2405. (7) Hansson, P.; Almeren, M. Lannmuir 1994, 10, 2115-24. (8) Chu, D.; Thomas,J. K. J. Am.Chem. SOC. 1986, 108, 6270-6. (9) Thalberg, K.; Lindman, B.; Bergfeldt, K. Langmuir 1991, 7,28938. (10) Satake, I.; Yang, J. T. Biopolymers 1976, 15, 2263-75. (11) Marcus, R. A. J. Phys. Chem. 1954, 58, 621-3. (12) Lifson, S. J. Chem. Phys. 1957, 26, 727-34. (13) Schwarz, G. Eur. J. Biochem. 1970, 12, 442-53. (14) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants: Physical Chemistry; Rubingh, D., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; Vol. 37. (15) Lofroth, J.-E.; Johansson, L.; Norinan, A.-C.; Wettstrom, K. Progr. Colloid Polym. Sci. 1991, 84, 78-82. (16) Manning, G. S. J. Phys. Chem. 1969, 51, 924-33. (17) Infelta, P. P.; Gratzel, M.; Thomas, J. K. J. Phys. Chem. 1974, 78, 190-5. (18) Tachiya, M. Chem. Phys. Lett. 1975, 33, 289. (19) Clint, J. H. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1327. (20) Hayakawa, K.; Santerre, J. P.; Kwak, J. Macromolecules 1983, 16, 1642- 5 . (21) Hayakawa, K.; Kwak, J. In Surfactant Science Series; Rubingh, D., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; Vol. 37. (22) Hayakawa, K.; Kwak J. J. Phys. Chem. 1982, 86, 3866-70. (23) Almgren, M.; Alsins, J. Progr Colloid Polym. Sci. 1987, 74. 5563. (24) Mukerjee, P.; Mysels, K. J. Nat. Stand. Ret Data Ser., Nat. Bur. Stand. (U.S.) 1971, No. 36, (25) Magny, B.; Iliopoulos, I.; Zana, R.; Audebert, R. Langmuir 1994, 10, 3180-7. (26) Bales, B. L.; Stenland, C. J. Phys. Chem. 1993, 97, 3418-33. (27) Wang, K.; Hansson, P.; Almgren, M. To be published. (28) Gao, Z.; Kwak, J. C. T.; Wasylishen, R. E. J. Colloid Interface Sci. 1988, 126, 371-6. (29) Hansson, P.; Almgren, M. J. Phys. Chem. 1995, 99, 16694. (30) Anderson, C. F.; Record, J. T. Ann. Rev. Phys. Chem. 1982, 33, 191-222. (31) Wei, Y. A.; Hudson, S. M. Macromolecules 1993, 26, 4151-4. (32) Okuzaki, H.; Osada, Y. Macromolecules 1994, 27, 502-6. (33) Hayakawa, K.; Fukutome, T.; Satake, I. Langmuir 1990.6, 14958. (34) How these values were obtained is not clear. The concentrations of surfactant and quencher together with the estimated average number of quenchers per micelle (from time-resolved fluorescence quenching) are not consistent with the reported aggregation numbers. See Table 4 in ref 25. (35) Dr. Jan Alsins, unpublished results. (36) Jones, M. N.; Piercy, J. J. Chem. Soc., Faraday Trans. 1 1972,68, 1839-48. JP95 1 155+