Aggregation and Microstructure in Aqueous Solutions of the Nonionic Surfactant C12E8

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

186, 170–179 (1997)

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Aggregation and Microstructure in Aqueous Solutions of the Nonionic Surfactant C12E8 D. DANINO,* Y. TALMON,*

AND

R. ZANA†,1

*Department of Chemical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel; and †Institut C. Sadron, CRM-EAHP, 6 rue Boussingault, 67000 Strasbourg, France Received July 5, 1996; accepted September 9, 1996

Mixtures of water and of the nonionic surfactant C12E8 (octaoxyethyleneglycol monododecylether) have been investigated by timeresolved fluorescence quenching (TRFQ) and transmission electron microscopy at cryogenic temperature (cryo-TEM) to obtain information on the size and shape of the surfactant aggregates and on the microstructure of the mixtures. The studies were performed at surfactant contents and temperatures where the micelles grew significantly and also where the systems undergo phase transitions from micellar-to-cubic upon increasing surfactant content or decreasing temperature and from cubic-to-hexagonal-to-micellar upon increasing temperature. No rapid change or discontinuity was observed in the variation of the aggregation number with the surfactant content or temperature upon crossing the micellar-tocubic phase boundary nor at the approach of the hexagonal phase from the cubic phase. The results confirmed that the cubic phase consists of spheroidal micelles forming a three-dimensional array. The aggregation numbers at high surfactant content or temperature can be much larger than that of the minimum spherical micelle for a surfactant with a dodecyl chain, suggesting that the micelles should be anisotropic. However, cryo-TEM showed that in the micellar phase the micelles are always spheroidal. These apparently inconsistent results are explained in terms of a partial mixing of the surfactant dodecyl chains and octaoxyethylene head groups which allows for spheroidal micelles of aggregation number much larger than for a surfactant with a dodecyl chain. The results show extensive exchange of material at 407C, taking place most likely via temporary merging of micelles in micelle clusters then present in the system. q 1997 Academic Press Key Words: nonionic surfactants; micelle aggregation number; shape and dynamics; micellar-to-cubic phase transition; cubic-tohexagonal phase transition; time-resolved fluorescence quenching; cryo-TEM.

INTRODUCTION

The self-association of nonionic surfactants of the polyoxyethyleneglycol monoalkyl ether type (denoted CmEn, where 1

To whom correspondence should be addressed.

170

0021-9797/97 $25.00 Copyright q 1997 by Academic Press All rights of reproduction in any form reserved.

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m is the carbon number of the alkyl chain and n the number of oxyethylene groups) has been extensively investigated in aqueous solutions (1–21). Most studies dealt with the effect of temperature, particularly the approach of the cloud temperature, Tc, above which CmEn solutions separate in two phases, in view of the importance of this effect in the actual uses of CmEn surfactants. The results below Tc have been diversely interpreted, in terms of either a very large growth (2–4), a moderate growth (5–19), or no growth at all of the micelles (20, 21). In the last case the observed changes of intensity of scattered radiation and micelle diffusion were attributed to the approach of a critical point. However, in most studies the results were interpreted in terms of a combination of both critical effects and micelle growth. It is now agreed that CmEn micelles grow with temperature, as shown in studies using time-resolved fluorescence quenching, a technique which provides a direct measure of micelle aggregation numbers and is not sensitive to critical effects, intermicellar interactions, and micelle shape (15–19). The growth mostly takes place in the range between Tc and a temperature about 30–407C below Tc. This temperature range widens as the surfactant concentration is increased (18, 19). The shape of the CmEn micelles has also been a topic of contention, with both oblate (4) and prolate (7, 11–14) shapes used in the interpretation of the results. It has been recently reported that close to Tc the micelles of some CmEn surfactants are thread-like and that their solutions behave like semi-dilute polymer solutions (12, 13). The thread-like micelles present in solutions of C16E6 have been visualized using transmission electron microscopy at cryogenic temperature (14). The phase behavior of binary mixtures of water and CmEn has been systematically investigated (1, 22). The phase diagram of the water–C12E8 (octaoxyethyleneglycol monododecyl ether) mixtures shows the presence of a large micellar phase L1 followed by a cubic phase I1, at low temperature, below 157C, and moderate concentration, between about 30 and 40% w/w (Fig. 1). This cubic phase is followed by a hexagonal phase H1 which is present up to 587C and between about 35 and 70% w/w at 257C. The cubic phase has been reported to consist of regularly arranged spheroidal micelles (22) but the variation of the micelle

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used pyrene as a fluorescent probe and dodecylpyridinium ion (chloride salt) as a quencher of the pyrene fluorescence (25). The samples of pyrene and dodecylpyridinium chloride were the same as in previous investigations (25). Methods

FIG. 1. Phase diagram of the C12E8/water system: L1, micellar solution; I1, spherical micelle cubic phase; H1, hexagonal phase; V1, normal bicontinuous cubic phase; La, lamellar phase; S, solid surfactant; W, dilute aqueous surfactant solution. The vertical lines indicate the compositions of the systems investigated. Reproduced from ref. 22 with permission of the Royal Society.

aggregation number in going from the micellar to such a cubic phase has been little investigated (23, 24). The change of the micelle aggregation number in the cubic phase at the approach to the cubic-to-hexagonal phase boundary has not been investigated thus far. The present study of the water–C12E8 mixtures addresses the above problems. Time-resolved fluorescence quenching (TRFQ) and transmission electron microscopy at cryogenic temperature (cryo-TEM) have been used to obtain information on the size and shape of C12E8 micelles in relatively dilute and in fairly concentrated micellar solutions, close to the micellar-to-cubic phase boundary. Also, the aggregation number of the micelles in the cubic phase has been measured up to a concentration close to the cubic-to-hexagonal phase boundary. The results show no discontinuity in micelle aggregation number when crossing the L1 –I1 phase boundary, and no large change of this number at the approach of the I1 –H1 phase boundary. The aggregation number in both the L1 and I1 phases increases with temperature, the more so at higher surfactant concentration. However, cryo-TEM shows only spheroidal micelles even at temperatures quite close to Tc, where anisotropic micelles should be present in the system, on the basis of the measured aggregation numbers. EXPERIMENTAL

Materials The sample of C12E8 was obtained from Nikko Chemicals Ltd. (Japan) and used as received. The fluorescence studies

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Cryo-TEM. The preparation of thin vitrified samples of the micellar solutions investigated in the controlled environment vitrification system (CEVS) and their handling at cryogenic temperature have been described (14, 26–28). Since the cubic and hexagonal phases do not flow, samples of these systems were prepared using ‘‘on-the-grid processing’’ (27, 29) and taking advantage of the known concentration gradient which exists in the thin-layer sample filling the holes of the grid, in going from the center to the wall of the holes (26–28). For the cubic phase, a drop of a 21.8% micellar solution was deposited on the holey grid and blotted in the CEVS which was operated at 97C and a relative humidity of 100%. The concentration gradient just discussed made the surfactant concentration near the edge of the holes that of the cubic phase. To produce the hexagonal phase, the initial concentration was 27%, the relative humidity less than 100%, and the temperature 257C. Slow controlled ‘‘on-thegrid’’ drying led to the hexagonal phase on the grid (see Fig. 1). The samples were then normally vitrified. On-thegrid processing sometimes allows the observation of intermediate (metastable) structures formed by crossing phase boundaries (29). The vitrified samples were studied at cryogenic temperature, typically 01707C, using a Gatan 626 cooling holder in a JEOL 2000FX transmission electron microscope, operating at 100 kV and nominal defocus of 4 mm. Printed micrographs were digitized using a Relisys 2412 scanner at 1024 dpi, and analyzed by the Digital Micrograph (version 2.5) software package (Gatan) on a Macintosh PowerPC 7100. Time-resolved fluorescence quenching. The pyrene fluorescence decay curves in the absence and in the presence of quencher were recorded using the previously described single-photon counting setup (30). The fluorescence decay curves were determined over about 1500–2000 ns, that is, a time duration about six times longer than the micellesolubilized pyrene lifetime, with a counting time sufficiently long that the last point of the experimental decay curves corresponded to at least 100 counts, after substracting the thermal noise. This procedure greatly reduced the error in the fitting parameters t, A2, A3, and A4 obtained by bestfitting the fluorescence decay Eqs. [1] and [2] (31–35) to the experimental decay curves determined in the absence and in the presence of quencher, respectively, using a weighted least-squares procedure (30).

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I(t) Å I(0)exp(0t/t)

[1]

I(t) Å I(0){0A2t 0 A3[1 0 exp(0A4t)]}

[2]

The pyrene fluorescence lifetime, t, the micelle aggregation number, N, and the pseudo-first-order rate constants, kq for intramicellar quenching, and km for probe and/or quencher intermicellar migration were obtained by inserting the values of the fitting parameters A2, A3, and A4 into Equations [3]–[5] (31–35):

TABLE 1 Values of the Pyrene Fluorescence Lifetime in the Absence of Quencher, t (in ns), and in the Presence of Quencher, 1/A2 (in ns), of the Micelle Aggregation Number, N, and of the Intramicellar Rate Constants of Quenching, kq (in s01) and of Intermicellar Migration, km (in s01) T (7C)

[3]

kq Å A4[1 0 (A2 0 1/t)/A3A4)]

[4]

km Å A4 0 kq

[5]

10 25a 40a

385.2 363.5 344.2

11.2 25a 39.8a

TRFQ. The aggregation numbers were measured as a function of temperature, T, at constant weight percent, w (vertical lines shown in the phase diagram in Fig. 1). Two systems (10.56% and 24.02% w/w, that is, 0.196 and 0.445 M, respectively) involved the micellar range. The system at 37.36% w/w (0.695 M) crossed the cubic-to-micellar phase boundary at around 157C. The last system at 41.24% w/w (0.765 M) crossed the cubic-to-hexagonal phase boundary at around 157C and the hexagonal-to-micellar phase boundary at around 487C, according to the reported phase diagram (Fig. 1). Notice that the temperatures corresponding to the phase transitions are not very accurately determined in the phase diagram in Fig. 1. Besides, this diagram does not show the biphasic regions separating the various monophasic ranges. Table 1 lists the values of the pyrene fluorescence lifetime in the absence of quencher, t, and in the presence of quencher, 1/A2, of the micelle aggregation number, N, of the rate constants kq, and km. Figures 2a and 2b show the variations of N and kq with T at constant surfactant weight percent, w, and Fig. 3 shows the variations of N and kq with w, at 10, 25, and 407C. In both figures the crossing of the micellar-to-cubic phase boundary brings no discontinuity or rapid change in the variations of N and kq, particularly when the boundary is crossed upon increasing w. This behavior confirms that the I1 cubic phase investigated consists of a three-dimensional ordered array of micelles which do not differ much, if at all, from the micelles in the isotropic phase, and that the L1 to I1 phase transition is similar to a liquid-to-solid transition, in the system investigated. Similar conclusions were reached for the micellar-to-cubic phase transition in dodecyltrimethylammonium chloride–water mixtures, also based on TRFQ (23, 24). It is noteworthy that at 107C the micelle aggregation number increases very little with surfactant content, in the range

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N

1006 kq

1006 km

376.7 350.2 318.4

90 99 117

4.50 7.70 9.84

0.09 0.13 0.26

4.45 7.03 6.59

0.09 0.21 0.46

3.43 4.12 5.07 5.51 4.72 3.95

0.15 0.13 0.13 0.28 0.53 1.11

3.44 4.31 3.80

0.11 0.15 3.09

24.02% C12E8 (0.445 M) a

RESULTS

1/A2

10.56% C12E8 (0.196 M) a

N Å A3[(C 0 cmc)/[Q]][1 / (A2 0 1/t)/A3A4]2

t

370.2 351.2 335.5

359.2 327.9 274.2

95 104 158

37.34% C12E8 (0.695 M) b

6 11.2b 17.5b 23a 29.7a 40a

375 369 360.6 355 347.4 335.5

362.5 357.4 348.5 327.6 292.5 221.3

94 99 104 120 158 244

41.24% C12E8 (0.766 M) b

8.9 14.7b 57.5a a b

369.4 364.9 316

359.3 352.6 134.7

97 106 381

Micellar solution. Cubic phase.

between 10.56% and 41.24%. A value close to 90 was previously reported for a 3% solution (15, 16). Such behavior indicates that the micelles are nearly monodisperse and, thus, close to spherical (36), in spite of their aggregation number being 90. Indeed, the aggregation number of the minimum spherical micelles formed by a surfactant with a dodecyl chain should be 55–60 (37). The value of 90 found for C12E8 micelles is thus apparently inconsistent with a spherical shape. At higher temperature the increase of N with w becomes more pronounced, the more so the higher the temperature. This may be taken as an indication that the micelle polydispersity increases, and that the micelles become more and more elongated as T or w are increased. The cryo-TEM results below show that this is not the case. Overall, the results for C12E8 in Figs. 2 and 3 are very similar to those for the mixtures of water and of C10E6 or C10E8 which show no phase transition up to 50% w/w (19, 38). Thus, the N vs T and kq vs T plots have the same shape for the three surfactants, with a positive curvature for the N

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FIG. 2. Variations of the micelle aggregation number N (a) and intramicellar quenching rate constant kq (b) with temperature. Surfactant concentration: (/) 3% (data from refs 15 and 16); (n) 10.56%; (s) 24.02%; (h) 37.36%; and (L) 41.24%.

plot and a maximum for the kq plot. This maximum is the result of two antagonistic effects (16, 19): (i) the normal increase of kq with T, predominant at low T (15, 16, 39), and (ii) the expected decrease of kq upon increasing micelle size (40), here upon increasing T, which becomes predominant at high T. Also, the results show that the rapid increase of N with T occurs at an increasingly lower T as the C12E8 concentration is increased, similarly to C10E6 and C10E8 (19). The results for the mixture at w Å 41.24% w/w in Fig. 2a show that at low temperature in the cubic phase (isotropic system) the aggregation number increases slowly with T between 9 and 157C. Between 20 and 267C the system was found to be biphasic with coexisting cubic and hexagonal phases, the latter detected through its birefringence between crossed polarizer and analyzer. The mixture was fully hexagonal between 26 and 507C. A micellar phase, coexisting with the H1 phase, appeared above 517C, and the mixture was

FIG. 3. Variations of the micelle aggregation number, N, with the C12E8 weight percent, w, at (l) 107C, (s) 257C, and (n) 407C. Most of the data were obtained by interpolating the results in Fig. 2a.

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completely micellar and not birefringent above 55.57C. An aggregation number of 381 was measured at 577C, but the error in this value is probably quite large, because of the extensive intermicellar exchange (migration) of probe or quencher taking place at such high w and T. In this work, intermicellar migration of probe or quencher was detected in micellar solutions of C12E8 (10.56% and 24.02% w/w) even at the lowest temperature used and also in the cubic phase, for the 37.36% w/w system (see Table 1). Within the experimental error, the exchange rate constant, km, remained small and independent of the surfactant content up to about 207C. In our study of C10E6 and C10E8 (19), no migration was detected up to 407C. However, the measurements used the tetradecylpyridinium ion as a quencher instead of the dodecylpyridinium. The latter has a residence time in surfactant micelles about 10 times shorter than the former (41), and pyrene has a residence time in the millisecond range (42). It is therefore likely that the small exchange observed below 207C involves only the dodecylpyridinium ion and occurs via its exit from C12E8 micelles, diffusion in the intermicellar solution and incorporation to another micelle (41). Migration via temporary merging of collided micelles is excluded, because it is characterized by values of km increasing with the surfactant content (34, 35), contrary to the experimental results. Also, it cannot take place in the cubic phase, which is solid (no micelle translation). At T ú 207C, km increases rapidly with T and with surfactant content, indicating the occurrence of intermicellar migration of probe or quencher via contacts between, and temporary merging of, micelles (15, 16, 19, 41). In dilute CmEn solutions, at T well below Tc, contacts occur via collisions between micelles (15, 16, 19). At higher T, the intermicellar interactions between CmEn micelles become increasingly attractive as T increases (5, 7, 43–46). The micelles tend to cluster, the more so the higher the temperature and surfactant concentra-

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allow a rapid intermicellar migration of probe and quencher, is presently being worked out (49, 50).

FIG. 4. Representative electron micrographs of vitrified samples of C12E8 micellar solutions showing spheroidal micelles. (a) 5% solution vitrified from 257C; (b) 5% solution vitrified from 757C; (c) 10% solution vitrified from 707C. Bar Å 100 nm.

tion (10, 47, 48). Within such clusters, intermicellar exchanges can easily take place between contiguous micelles, no longer requiring micellar collisions. The exchange process is then described by a true first-order rate constant, km, which represents the rate constant for temporary merging of contiguous micelles and which depends strongly on both temperature and concentration as these parameters determine the average size of micelle clusters. The theory for timeresolved fluorescence quenching in such systems, which

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Cryo-TEM. Electron micrographs of a 5% micellar solution of C12E8 vitrified from room temperature show only small spherical or spheroidal micelles (Fig. 4a). Small spherical micelles are also seen in 5% and 10% samples vitrified from 70 and 757C (Figs. 4b and 4c), respectively, that is, from temperatures close to the cloud point. Note that the real quenching temperature of the TEM samples is probably a few degrees lower due to cooling taking place while the sample rapidly travels between the CEVS and the liquid ethane reservoir (51). Nevertheless, even if the vitrification temperatures are about 107C below Tc, large objects are expected to be seen as the micelles start growing some 357C below Tc (15). Thus, the presence of spheroidal micelles is surprising in view of the large dimensions of the C12E8 molecule (the octaoxyethylene head group is much larger than the head group of usual ionic surfactants). It is also inconsistent with the values of the aggregation number found for C12E8 micelles (Table 1). However, the observation of spheroidal micelles both at room temperature and close to Tc is in agreement with a small-angle neutron-scattering study of a 1.5% C12E8 solution in the temperature range of 20–74.27C, which suggested polydisperse spherical micelles, whose sizes increase little with temperature (52). It also agrees with the results of Corti et al. (53) who found little variation of micelle size and shape throughout that temperature range. Those authors also reported that the micelles remain spherical and retain nearly a constant size when approaching the hexagonal phase (up to 30% at 307C, see Fig. 1), in agreement with our TRFQ and cryo-TEM results. Taken together, these results suggest that the micellar-to-hexagonal phase transition in the C12E8/ water system involves changes in the micelle structure combined with an order–disorder transition. The aggregation number, Nsph, of the minimum spherical micelles for a surfactant with a dodecyl alkyl chain is 55– 60 (37). However, the aggregation number of C12E8 micelles is about 90 at low T and increases significantly with temperature. For instance, N Å 300, for a 3% C12E8 solution at T Å 657C (15, 16). The value of N is likely to be much larger for the more concentrated solutions investigated here. Thus the micelles should be seen by cryo-TEM as anisotropic objects, with an axial ratio approximately equal to N/Nsph, that is, larger than 5. Experimentally, this is not the case for C12E8 (Figs. 4a–c) and also for C10E6 and C12E6 (54). A possible explanation for this apparent inconsistency between TRFQ results and cryo-TEM observations is given in the Discussion, below. The cubic and hexagonal phases were also visualized by cryo-TEM. Vitrified samples of these phases were prepared by on-the-grid-processing as indicated in the Experimental Sec-

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tion. Figures 5a and 5b show representative cryo-transmission micrographs of the cubic phase. The arrows point to several ordered structures which correspond to grains of different orientations. One has to bear in mind that these are two-dimensional projections of a three-dimensional structure. Figure 6a is a representative micrograph of the hexagonal phase prepared on the grid. The cryo-TEM image shows an area with long parallel lines, indicating an ordered structure, namely, the hexagonal phase viewed perpendicularly to the long axis of the thread-like micelles that make it up. What we see in the micrograph are not individual micelles but the projection of aligned stacks of micelles. This alignment may be caused by the thinning of the liquid film during specimen preparation (27). To try to glean more information from the micrograph we used Macintosh computer-based image analysis. Figure 6b is a digitized portion of the micrograph in 6a. The Fourier transform of the image in 6b, calculated by the software program, is displayed in Fig. 6c and shows two pairs of reflections, denoted ‘‘1’’ and ‘‘2’’. By constructing an appropriate mask, one can use only selected spatial frequencies to be used in the inverse Fourier transform (IFT), which leads to a ‘‘filtered’’ image. Figure 6d is such an IFT using the pair of reflections ‘‘1’’ of Fig. 6c, while Fig. 6e is the IFT of 6c using the pair of reflections ‘‘2’’. The superposition of the two structures in 6d and 6e, constructed as the IFT in Fig. 6f, using both reflection pairs is the filtered image of 6b. Note that Fig. 6d and 6e show similar structures of the hexagonal phase that are tilted with respect to each other. These may represent two meso-crystals that started growing from opposite sides of the liquid film prior to vitrification. Note also the dislocations clearly visible in the filtered images (arrows in Figs. 6d and 6e). The dark and light patches seen in the filtered image (Figs. 6d–f) are the result of thickness variation of the specimen. DISCUSSION

We have pointed out above that the micelles of CmEn surfactants are seen by cryo-TEM as small spheroidal objects, even at temperatures less than 107C below Tc. This observation is not consistent with the values of the aggregation numbers of CmEn micelles, values which at 407C, that is, some 387C below Tc, are more than 5 times larger than for the minimum micelle with a spherical hydrophobic core of radius equal to the length of the dodecyl chain in its fully extended conformation. Besides, the TRFQ experiments indicated that the polydispersity of CmEn micelles remained relatively small even when the aggregation numbers were rather large. For instance, for C10E8 at 50% and 507C, N Å 250, but the standard deviation, s, was only 80, and the distribution of aggregation numbers appeared to be nearly Gaussian (19). A possible explanation for these seemingly inconsistent

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results is that alkyl chains and polyoxyethylene groups can partially mix or interpenetrate in an intermediate shell of a thickness that increases with temperature. The micelles would then present three regions: a hydrocarbon core, a mixed shell of alkyl and polyoxyethylene groups, and an outer shell of polyoxyethylene groups. Such a mixed shell has been used to explain viscosity and light scattering data for Triton X-100, an ethoxylated nonionic surfactant (55). The presence of this intermediate shell is equivalent to dealing with a surfactant with an effective carbon number which can be much larger than that of the surfactant alkyl chain. It permits the packing of a larger number of surfactants into spherical micelles. The existence of the intermediate shell can be justified on the grounds that polyoxyethylene is not completely insoluble in alkanes (56) and that its solubility in alkanes probably increases with temperature as it then becomes less polar. That explains its upper consolute point and the clouding phenomenon in aqueous solutions (57–60). If the effective carbon number of the surfactant is larger by 3 or 4 units, the value of Nsph would be almost doubled for C10En surfactants, to about 80, and increased by over 60% to 95 for C12En surfactants. These values are close to those found for such surfactants at T well below Tc (15, 16, 19). However, owing to their spheroidal shape, the micelles would be only little polydisperse, in spite of their large aggregation numbers. At higher T, the micelles grow, but their axial ratio remains small, 2 or 3 at the most, as based on the values of N and effective Nsph. The latter is indeed expected to increase with temperature because of the increased mixing of alkyl chains and polyoxyethylene groups. CryoTEM cannot distinguish between elongated micelles of such low elongation and spherical micelles. At this stage, recall that the electron contrast between water and alkyl chains is larger than between water and polyoxyethylene groups. This may explain that in the electron micrographs the visualized CmEn micelles appear to be somewhat smaller than micelles of ionic surfactants, where the ionic groups strongly contribute to the dimension of the visualized micelles, owing to their large electron contrast relative to water (61). The existence of a mixed shell of alkyl and polyoxyethylene groups and its expected thickening with temperature can only further enhance this aspect. Finally, in agreement with our observations, a study of ethoxylated diisononylphenol surfactants (62) reported spherical micelles with an aggregation number of 430, that is much larger than for a surfactant having this type of hydrophobic group. Another point of discussion concerns the values of the aggregation numbers determined by TRFQ. Close to the cloud temperature, CmEn micelles form clusters (10, 47, 48). In fact, the high values found for the first-order rate constant of intermicellar exchange, km, at high temperature in this study and in others of similar surfactants (15–19) provide evidence for such clusters. Nevertheless, the analysis of the

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FIG. 5. Cryo-transmission electron micrographs of vitrified samples of the cubic phase of C12E8. This phase was formed due to the concentration gradient existing between thin and thick regions on the grid (see Methods in the Experimental). Arrows point on the direction of repeating structure, seen as ordered parallel lines. Bar Å 100 nm.

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FIG. 6. The hexagonal phase of C12E8 prepared on the grid: (a) a cryo-TEM image showing an area of ordered structures (bar Å 100 nm), (b) a digitized portion of the micrograph in a (bar Å 50 nm), (c) the Fourier transform of the image in b; note two pairs of reflections denoted ‘‘1’’ and ‘‘2’’; (d) the inverse Fourier transform (IFT) of c using the pair of reflections ‘‘1’’; (e) IFT of c using the pair of reflections ‘‘2’’; (f) superposition of the two structures in d and e, which corresponds to a filtered image of b.

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fluorescence decay curves, which led to the values of N in Table 1, used equations which assumed discrete micelles, and neglected the presence of micelle clusters, which may greatly facilitate intermicellar exchanges. We did so because the theory for systems containing clusters of micelles is still being elaborated (49, 50). The equations used represent a good first approximation. Nevertheless they may lead to overestimated N values in situations where micelles cluster, that is, at high T. If that is the case at high T, the micelles would be even less elongated than discussed above, and TRFQ results and cryo-TEM observations the more consistent. CONCLUSIONS AND SUMMARY

The present investigation dealt with several aspects of the aggregation of C12E8 in aqueous solution and the microstructure of these systems. We showed that the aggregation numbers hardly changed when crossing the phase boundary separating the micellar phase of C12E8 and its cubic phase which consists of regularly arranged nearly spherical micelles. No gross change in aggregate property was noted when approaching the cubic-to-hexagonal phase boundary. The cryoTEM experiments showed that the micelles of C12E8 are spherical or spheroidal even at T close to the cloud temperature. This observation is inconsistent with the rather large values of micelle aggregation numbers measured for C12E8, at high T. This apparent inconsistency can be understood by assuming a partial mixing of alkyl chains and polyoxyethylene groups in C12E8 micelles, in a shell of thickness increasing with temperature. This allows C12E8 and probably other similar ethoxylated nonionic surfactants to form spherical or spheroidal micelles much larger than anticipated on the basis of their alkyl chain carbon number. The analysis of the fluorescence decay curves by means of current models also needs refinement in order to take into account the fact that the micelles tend to cluster at T close to Tc. ACKNOWLEDGMENTS The work done at the Technion was supported in part by grants from the United States—Israel Binational Science Foundation (BSF), Jerusalem, and from the Fund for the Promotion of Research at the Technion. The authors thank Ms. Berta Shdemati and Judith Schmidt for expert technical help and assistance. R.Z. thanks the Mission des Relations Internationales (CNRS, France) for partial financing of his stay at the Technion.

REFERENCES 1. Degiorgio, V., in ‘‘Physics of Amphiphiles: Micelles, Vesicles, and Microemulsions’’ (V. Degiorgio and M. Corti, Eds.), p. 303. NorthHolland, Amsterdam, 1985. 2. Balmbra, R. R., Clunie, J. S., Corkill, J. M., and Goodman, J. F., Trans. Faraday Soc. 58, 1661 (1962).

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