J. Phys. Chem. 1994,98, 6607-6611
Ultrasonic Absorption Studies of Surfactant Exchange between Micelles and the Bulk Phase in Aqueous Micellar Solutions of Amphoteric Surfactants M. Frindi and B. Micheis Laboratoire d'Ultrasons et de Dynamique des Fluides Complexes (LUDFC), URA 851 du CNRS, Universiti Louis Pasteur, 4, rue Blaise Pascal, F-67070 Strasbourg Cedex, France
R. Zana' Institut Charles Sadron (CRM-EAHP), CNRS- ULP, 6, rue Boussingault, 67083 Strasbourg Cedex, France Received: February 16, 1994"
The kinetics of surfactant exchange between micelles and the bulk phase has been investigated by the ultrasonic relaxation absorption method in aqueous solutions of the two amphoteric surfactants: the n-octyl and n-decyl (dimethylammonio)propanesulfonates, referred to as 8DAPS and 1ODAPS, respectively. Complementary determinations of critical micelle concentration, micelle aggregation number, and isothermal volume change upon micellization have been performed using spectrofluorometry (with pyrene as probe), ultrasonic absorption, time-resolved fluorescence quenching, and density measurements. The ultrasonic relaxation results support the model of Aniansson and Wall for the surfactant exchange. As for ionic and nonionic surfactants, the rate constant for the incorporation of amphoteric surfactants into the micelles is found to be above 109 M-1 s-1, indicating that this process is nearly diffusion-controlled. The spectrofluorometric results suggest that the pyrene molecules solubilized in the 8DAPS and 1ODAPS micelles reside close to the positively charged nitrogen atom.
Introduction The micelles which are present in aqueous solutions of amphiphiles (surfactants) at concentrations above the critical micelle concentration (cmc) are not frozen assemblies. They constantly exchange amphiphiles with the bulk (intermicellar) phase, and these exchanges can be represented by the chemical equilibrium A,
* A,, + A
where Ai and Ai-] are micelles made of i and i - 1 amphiphiles A, respectively. The kinetics of these exchanges has been extensively investigated for a variety of ionic and nonionic surfactants.'V2 The theoretical treatment for surfactant exchange kinetics of Aniansson and Wall,3 which has been further improved by Lessner et al.' and Hall? has been shown to give a very satisfactory account of the results,'I2 except in the case of a peculiar class of complex biological surfactants, the gangliosides.6 It is generally found that the rate constant k+ for the incorporation of a surfactant into a micelle is close to that for a diffusion-controlled process's2 (Le., the rate of incorporation is close to the rate of collisions between free surfactants and micelles). The rate constant of exit of a surfactant from a micelle is strongly dependent on the surfactant hydrophobic moiety and decreases by a factor of about 3 per additional methylene group in the surfactant alkyl A survey of the literature revealed that there has been no study of the kinetics of the exchange process (1) for amphoteric surfactants in aqueous solutions. In view of our current interest in studying the kinetics of the exchange process for unusual surfactantseries,z'we haveundertakensuch a study in the aqueous solutions of two amphoteric surfactants: the n-octyl and n-decyl (dimethylammonio)propanesulfonates,referred to as 8DAPS and lODAPS, respectively. These two surfactants were selected because (i) they are commercially availableor can be easily synthesized and purified,*
* To whom correspondence should be addressed.
Abstract published in Adounce ACS Absfructs. June 1, 1994.
(ii) they have been fairly well investigated, at least lODAPS,"lS and in particular, their cmc's have been found to be much higher than expected for surfactants with a zero net charge, and (iii) they have a very bulky head group, of dipolar nature, which may affect the kinetics of their exchanges. The measurements reported below concern determinations of cmc by spectrofluorometry, using pyrene as a probe, and ultrasonic absorption measurements,2of micelle aggregation number, N , by time-resolved fluorescence quenching1618 and of isothermal volume change upon micelle formation, AVP, through density measurements,2 in addition to the kinetic study which was performed by the ultrasonic absorption relaxation method.182 Recall that this method can be used only with surfactants having a relatively short alkyl chain and/or a cmc 1 10-20 mM. The cmc and N values are required for the full analysis of the relaxation data, and the cmc values were determined as part of this work as the reported values for 8DAPS show large differences. The analysis of the ultrasonic relaxation amplitudeyields the isentropic volume changeupon micellization, AVsO, which can be compared to AVP. The two values should not differ much in aqueous solutions at 25 OC. It is shown below that the rate constants for the exchange process in 8DAPS and lODAPS solutions are well in line with those previously determined for ionic and nonionic surfactants. The theory of Aniansson and Wall gives a good account of the results.
Experimental Section Materials. 8DAPS and lODAPS were purchased from Sigma Chemicals and recrystallized three times from a mixture of acetone-ethanol. The purity of the surfactants, checked by elemental analysis, was at least 99%. A sample of 8DAPS, synthesized and purified as reported by Fendler et a1.,8 gave the same elementalanalysis and kinetics results as the purified Sigma sample. Pyrene was the same as in other studies.2 Methods. The cmc's were determined by spectrofluorometry from the plots of the ratio 1 1 / 1 3 of the intensities of the first and third vibronic peaks in the fluorescence emission spectrum of 0 1994 American Chemical Society
Frindi et al.
6608 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994
1 : -
C(mW Figure 1. Variation of a/p (0)and of I l / I 3 concentration for 8DAPS.
with the surfactant
pyrene solubilized at very low concentration (5 X 10-7-106 M) in the surfactant solutions2 versus the surfactant concentration C. The fluorescence spectra were recorded using a Hitachi F 4010 spectrofluorometer, at an excitation wavelength of 335 nm and a bandwidth of 1.5 nm both at the excitation and emission. The plots of the ultrasonic absorption a/f (a = absorption coefficient,f = ultrasonic frequency) versus C, at a constant and sufficiently low frequency (f 0.7 MHz), were also used for cmc determination^.^ The isothermal volume change upon micellization AVf was obtained from the plot of the apparent molal volume 4~ against C.2 The #V vs C plots were also used to determine the cmc of the surfactants. The densities required for obtaining the values of $JV were measured with an Anton-Parr DMA 60 densimeter. The micelleaggregationnumbers were obtained using the timeresolved fluorescence quenching methodl6lS with pyrene as fluorescenceprobe and dodecylpyridiniumchloride as quencher. The fluorescencedecay curves were obtained using the same singlephoton-counting setup as previously.2 The ultrasonic absorption a/f was measured using the same two setups as in recent studies. The ultrasonic relaxation spectra were analyzed as previously describeda2 All measurements were performed at 25 OC.
C(mM) Figure 2. Variation of a//2 (B) and of concentration for IODAPS.
(+) with the surfactant
TABLE 1: Cmc'q Isothermal Volume Changes upon Micelle Formation, and Micelle Aggregation Numbers for 8DAPDS and lODAPS surfactant cmc (mM) AVP (cm3mol-') N 8DAPS 265O 4.1J 23 3 at 500mMJ
3356 272c 160," 375,e330' lODAPS 38" 37.56 33.7c 37,d 42,s40f 39h
4 at 60 mMJ * 4 at 80 mMJ 41 at cmG
3.41 3.6-4.7,c 3.9'
From the a/f2vs Cplots. From the Il/I3 vs C plots. From the &V vsCplots. Fromref 12. e Fromref 14. fCalbiochemcatalogue;8DAPS is listed under Zwittergent 3-08. From ref 13. From ref 9. From ref 10. This work. 0
Results and Discussion CMC. Figure 1 shows thevariationof1~/13andoftheultrasonic absorption a/f with the 8DAPS concentration. The corresponding results for lODAPS are shown in Figure 2. The a/f plots clearly define the cmc obtained by a short extrapolation, as shown in Figures 1 and 2 with values 280 and 37 mM for 8DAPS and 10DAPS. The cmc is clearly seen in the 11/13 vs C plot for lODAPS at 34 mM, in good agreement with the ultrasonic value (Figure 2). On the contrary, for 8DAPS the decrease of 11/13 stretches between 200 and 400 mM, i.e. starts below and goes on well above the cmc value obtained by ultrasonic absorption. The usual extrapolation method yields a cmc value of 335 mM, about 20%larger than the ultrasonicvalue, but in agreement with some of the reported values (Table 1). This is the first instance that such a large difference is observed between the two methods used. It may be related to the fact that the 8DAPS micelles are rather small (see below). Nevertheless, the density data below as well as the ultrasonic absorption relaxation data clearly show that the cmc of 8DAPS is 280 k 20 mM. Isothermal Volume Change, A V+'. The apparent molalvolumes 4~ for the two surfactants calculated from the density data are represented in Figure 3. The curves in solid lines represent best fits of the equation2
C(mW Figure 3. Variation of the apparent molal volume of 8DAPS (0)and of lODAPS (m) with the surfactant concentration. The curves going through the experimental data have been calculated as indicated in the text.
dv = dv,ccmc +
AV;(C- cmc) C
to the experimental results, with AVf as an adjustable parameter, qt~v,~,,,~ is the apparent molal volume at the cmc. The cmc and 4v,- values have been taken as 272 and 33.7 m M and as 247.6 and 281.8 cm3 mol-' for 8DAPS and lODAPS, respectively. The fits are seen to be satisfactory and yield the AVf values listed in Table 1. Our AVf values agree well with the reported data. Note that the fit of eq 2 to the 8DAPS data, using a cmc value
Surfactant Exchange between Micelles and Bulk Phases of 320 mM, was of bad quality. The 4Up values obtained by extrapolating the 4~ data below the cmc to C = 0 are 248.7 f 0.5 and 281.8 f 0.5 cm3 mol-' for 8DAPS and lODAPS, respectively. The difference yields a partial molal volume increment per methylene group of 16.5 f 0.5 cm3 mol-', in good agreement with the reported value.19 Also our values for 69 agree with reported ones.I0 In the case of 8DAPS, where the cmc is high, the results show a decrease of 4Up upon increasing C, up to the cmc. This behavior is typical of aqueous solutions of hydrophobic solutes and surfactants with a high cmc,2e23 It is generally attributed to the effect of the solute alkyl chain on the structure of water (hydrophobic solvation). Micelle Polarity. The 11/13 values at high C, when all of the pyrene is solubilized in the micelles, are 1.60and 1.5 1 for 8DAPS and IODAPS, respectively. The value = 1.47 has been obtained for 12DAPS, as part of this work. Correlatively, the values of the pyrene fluorescence lifetime, T , in deaerated aqueous micellar solutions of these three surfactants have been found to be 271, 325, and 340 ns, respectively. Recall that the values of Zl/Z3 and of T give a measure of the polarity sensed by pyrene at its solubilization site.'6 Thus, these values reveal that in 8DAPS micelles extensive contacts occur between pyrene and water, resulting in a high polarity, probably because of the small micelle size (see below) and loose packing of the alkyl chains. The results also indicate that the polarity sensed by pyrene decreases as the surfactant chain length increases. This is in relation to the increase of the micelle aggregation number with surfactant chain length (see below) and lesser contacts between pyrene and water. Notice that the Z,/Z3 values found for the surfactants investigated are high, higher for instance than for alkyl sulfates (Zl/Z3 = 1.21 for sodium dodecyl sulfate) and for noninoic surfactantsa2Besides, they are close to those found for the n-alkyltrimethylammonium bromides: 1.56 for the n-octyl, 1.45 for the n-decyl, and 1.42 for the n-dodecyl, measured as part of this work under the same experimental conditions as for the two amphoteric surfactants. The similarity in the Zl/Z3 values found for the amphoteric surfactants and the corresponding alkyltrimethylammonium bromides probably indicates that in nDAPS micelles pyrene is preferentially located close to thecharged nitrogen atom, possibly because of an attractive electrostatic interaction between this atom and the *-electron cloud surrounding pyrene. Aggregation Numbers. The pyrene concentration used in the fluorescence decay experiments was around 2 X 10-6 M. The quencher concentration was adjusted to reach a [quencher]/ [micelle] molar concentration ratio close to 1. Quencher migration was found to occur, as indicated by the longer pyrene fluorescence lifetime measured in the absence of quencher as compared to that in the presence of quencher. The full equations (case of the mobile quencher2'26) were therefore used for the analysis of the decay curves. Nevertheless, owing to the high quencher concentration, the correction for migration was small. The values of the aggregation numbers are listed in Table 1. They are rather close to those which can be calculated from the oil drop model, which assumes a micelle hydrophobic core of radius equal to the length of the alkyl chain in its fully stretched conformation.27~28This model leads to values of 27 and 40 for the aggregation numbers of micelles of surfactants with octyl and decyl alkyl chains. Note also that the aggregation numbers found for the two amphoteric surfactants are much smaller than those reported for nonionic ethoxy surfactants of the C,E, type ( n = number of carbon atoms; E = ethoxy group), around 100 for C10Em29( m = 6,8) and around 80for CsE5,2.30at temperatures far below the cloud temperature. This comparison reveals that the nDAPS surfactants have an aggregation number closer to that of ionic surfactants than to that of nonionic surfactants of equal alkyl chain length. Kinetics of Surfactant Exchange. Figure 4A shows typical
The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 6609 2000
Figure 4. (A) Top: Ultrasonic absorption spectra of SDAPS at 25 ' C for solutions 500 mM (0),400 mM (A),350 mM (X), and 250 mM ( 0 ) . The solid lines represent the calculated curves best fitting eq 3 to the data. (B)Bottom: Ultrasonic absorption spectra of lODAPS at 25 O C for solutions 100 mM (v)70 mM (H), 50 mM (A),and 35 mM (+). The solid lines represent the calculated curves best fitting eq 3 to the data.
ultrasonic relaxation spectra for 8DAPS. The solid curves going through the experimental results have been calculated by fitting the relaxation equation for a single relaxation time process
(3) to the experimental data using a weighted least-squares procedure.2 In eq 3, A is the relaxation amplitude. The relaxation frequencyfR is related to the relaxation time TR according to fR = (2*7R)-'. B is a constant which should not differ much from the value of a/f2 for the solvent, here water (a/$ = 21.5 m-' s2 at 25 'C2). The experimental results clearly show the lowfrequency plateau (at f << fR, a/$ = A B), which greatly improves the quality of the fitting. Unfortunately the situation is much less favorablefor 1OD-, as can be seen in Figure 4B. There the low-frequency plateau is not reached in the frequency range investigated. Even if the fits of eq 3 to the experimental results (solid lines in Figure 4B) look good, the error on A and fR can be rather large because the values of fR are outside, or at the lowest limit, of the frequency range investigated. These errors are difficult to appreciate, and the A and fR values for IODAPS cannot be given more than a semiquantitative meaning. Note that the values of A and fR obtained from the fitting procedure are correlated, with larger values of A corresponding to lower values of fR.
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6610 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 20 11 I 10
2.0 k l
-9 - 8
L I I
0 2 1
' '3 600
C(mM) Figure 6. Variations offR with (C- cmc)/cmc (X) and A ~ with R C ~ (0) for 8DAPS.
surfactant (mM) 8DAPS
350 400 500 600 lODAPS
35 40 50 60 70 80 100
14 400 840 1265 1705 1670 43 1115 1380 1710 1860 1880 1840
24 27 28 29 40 50 21 24 22 22 23 23 24
d 10-50 (Hz) (g ~ m - ~ )(cm s-l)
lodf~ 9.54 5.06 6.08 6.81 8.12 10.00 6.05 0.40 0.65 0.84 0.98 1.16 1.48
0.998 542 1.006641 1.008080 1.009601 1.012397 1.015335 0.997 968 0.998089 0.998295 0.998534 0.998761 0.998996 0,999440
1.549 1.557 1.560 1.564 1.569 1.580 1 SO7 1 SO7 1.508 1.509 1.509 1.510 1.506
ThevaluesofA, B,andfRobtainedfor thesolutions investigated are listed in Table 2. The values of B are close to that of water as expected, except for the most concentrated solutions of 8DAPS (C 1 400 mM). Thus for the investigated amphoteric surfactants the exchange process is characterized by a single relaxation time, as for ionic1 and nonionic2 surfactants. The relaxation time TR and amplitude A are given by3.31332
- 1= 2 4 = ; ; I k-( 1+--)u2 C-cmc N cmc TR
where d is the density of the solution (g cm-3), u the velocity of ultrasound in the solution (cm s-I), R the gas constant (8.32 X lo7 ergs mol-' deg-I), T the absolute temperature, AVso the isentropic volume change upon micellization (cm3 mol-'), and k the rate constant (s-l) of exit of a surfactant from the micelle proper, of aggregation number N. The rate constant k+ (M-I s-I) for the incorporation of a surfactant into the micelle of aggregation number N is given by
Equations 4 and 5 predict a linear variation of fR and AfR2 with the surfactant concentration C at C > cmc. This prediction is borne out by results plotted in Figures 6 and 7 , where all straight solid lines going through the data have been obtained by a weighted
Figure 7. Variations OffR with (C- cmc)/cmc (+) and A ~ with R C ~ (W) for 10DAPS.
least-squaresprocedure.2 These results confirm that the observed relaxation process arises from the surfactant exchange between micelles and intermicellar solution. Figure 5 shows the increase offR upon decreasing C,at Cslightly below cmc, already observed for a number of other surfactants with a high cmc value and attributed to processes involving oligomeric aggregates.* The extrapolations of the AfR2 plots in Figures 6 and 7 intercept the C axis at the cmc. The cmc values thus determined, 265 and 38 mM, for 8DAPS and lODAPS, respectively, are in good agreement with those from the Z l l Z 3 vs C plots for lODAPS and from the a/fZ vs C plots for both surfactants. The results in Figures 6 and 7 have been analyzed on the basis of eqs 4-6 using the values of d and u in Table 2, measured as part of this work. The values of k/a2 and k / Nobtained as the intercepts and slopes of the plots in Figures 6 and 7 and of $IN, k, k+,and Q obtained using the values of N in Table 1 are listed in Table 3. The values of k+ are above 109 M-1 s-l, indicating that the incorporation of the amphoteric surfactants investigated is nearly diffusion-controlled,as found for a variety of ionic' and noninoic surfactants.2 The difference between the k+ values for 8DAPS and lODAPS cannot be given much significance because of the large error which may affect the lODAPS data (see above). The value of k for 8DAPS is quite high, but this is in line with the high cmc value of this surfactant.
The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 6611
Surfactant Exchange between Micelles and Bulk Phases
TABLE 3: Values of k/& k / N , u2/N, k, kt, a, and AVso at 25 OC for the Investigated Surfactants
A Vso 10-6k/uz IWk/N 1Vk lo-%+ surfactant (8') (s-l) u2/N (d) (m-l s-I) 4.3a 1.6b 32.5 18.5 0.6 8DAPS 4.25 1.6 1.7O 4Sb lODAPS 2.72
(cm3 u mol-') 4' 8O
The calculation of k from k / N and of u from 0 2 / Nused N values of 23 and 40 for 8DAPS and IODAPS. The calculation of &+ from k / c m c used cmc values of 265 and 38 mM for 8DAPS and IODAPS.
Finally it is seen that the AVso values are around 8 em3 mol-' for the two surfactants and well above the AVf values., The difference appears to be larger than expected from the experimental errors on both quantities.
Conclusions We have investigated the kinetics of the exchange of two amphoteric surfactants, the n-octyl and n-decyl (dimethylammonio)propanesulfonates,between micelles and the bulk phase. The results are very similar to those for ionic and nonionic surfactants. In particular, the rate constant of incorporation of the surfactant into the micelles is nearly diffusion-controlled. The micelle aggregation numbers of the two surfactants have been found to be close to those for ionic surfactants with the same alkyl chain, revealing that in spite of their zero net charge the amphoteric surfactants investigated behave like charged ones. Spectrofluorometric investigations indicate that the pyrene solubilized in the micelles is preferentially located near the charged nitrogen atom of the surfactant head group.
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