Segregation in Aqueous Mixtures of Nonionic Polymers and Surfactant

Nov 8, 1995 - The phase behavior at different temperatures was studied for aqueous mixtures of the polymers dextran T70 or poly(ethylene oxide) 40000 ...
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J. Phys. Chem. 1996, 100, 3675-3679

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Segregation in Aqueous Mixtures of Nonionic Polymers and Surfactant Micelles. Effects of Micelle Size and Surfactant Headgroup/Polymer Interactions Lennart Piculell,* Karin Bergfeldt, and Stina Gerdes† Physical Chemistry 1, Lund UniVersity, Box 124, S-221 00 Lund, Sweden ReceiVed: July 14, 1995; In Final Form: NoVember 8, 1995X

The phase behavior at different temperatures was studied for aqueous mixtures of the polymers dextran T70 or poly(ethylene oxide) 40000 (PEO) with the surfactants penta(ethylene oxide) dodecyl ether (C12E5), octa(ethylene oxide) dodecyl ether (C12E8), or n-octyl-β-D-glucopyranoside (C8G1). At sufficiently high concentrations, a segregative two-phase separation, with the polymer and the sufactant being enriched in different phases, was found for all polymer/surfactant couples. The segregation became stronger with increasing size of the surfactant micelle. Micellar growth was considered to be the major factor governing the rapid growth of two-phase area with increasing temperature in mixtures involving C12E5 (at all temperatures) and C12E8 (above room temperature). In contrast, under conditions of approximately constant micellar sizes, the two-phase area decreased slightly with increasing temperature. Short-range interactions between the surfactant headgroups and the polymers were found to be important for the extent of the segregation. The chemically similar couples dextran/C8G1 and PEO/C12E8 were more miscible than the dissimilar couples dextran/C12E8 or PEO/C8G1, but the opposite trend was found for the mixtures involving C12E5.

Introduction Interactions between polymers and micelle-forming surfactants in aqueous solution are currently attracting much interest. Most studies to date have been concerned with cases where there is a net attraction between the polymer and the surfactant micelle.1,2 Especially for oppositely charged polymer/surfactant pairs, the attraction may result in an associatiVe phase separation, where one concentrated phase, enriched in both polymer and surfactant, exists in equilibrium with a phase that is dilute in both solutes.2 The (presumably more common) repulsive polymer/surfactant couples have only just begun to be explored. Sufficiently concentrated mixtures of the latter type are expected to phase-separate segregatiVely into two phases of comparable solute content, but where one phase is enriched in the polymer and the other in the surfactant.2 The latter behavior has been confirmed in a few recent studies.2-7 For practical purposes, segregating polymer/surfactant couples could be useful in contexts where segregating polymers are now being used, such as aqueous two-phase partitioning8 and mixed polymer gels.9 More systematic studies on the polymer/surfactant mixtures are needed, however, in order to map out general trends and, ultimately, to arrive at a more detailed molecular understanding of their phase behavior. Segregation has been documented in various combinations involving both ionic and nonionic polymers and surfactants. Wormuth3 studied nonionic surfactants of the alkyl oligo(ehylene oxide) (CnEm) type in mixtures with short and long chains of poly(ethylene oxide) (PEO). He found a segregative phase separation in mixtures of the micelle-forming surfactant C8E4 with PEO 20 000. Thalberg et al.4-6 studied mixtures of the anionic polysaccharide sodium hyaluronate with ionic surfactants. For cationic surfactants, segregation only occurred at high concentrations (ca. 0.5 M and above) of added salt, whereas mixtures with the anionic surfactant sodium dodecyl sulfate segregated even in the absence of salt. In a preliminary study, two of the present authors found segregation in mixtures of † Present address: Institute for Surface Chemistry, P.O. Box 5607, S-114 86 Stockholm, Sweden. X Abstract published in AdVance ACS Abstracts, January 15, 1996.

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C12E8 or C12E5 with dextran or with PEO,2 and recently Clegg et al.7 published a study demonstrating a segregative phase behavior in a variety of mixtures of ionic or nonionic polymers with the nonionic surfactants C10E6 and C13E7. Another relevant study is the very recent work by Svensson et al., who studied the segregation in aqueous mixtures of dextran with micelleforming triblock copolymers of the PEO-poly(propylene oxide)-PEO type.10 The studies performed to date have shown, not unexpectedly, that the segregative two-phase area increases with increasing molecular weight of the polymer2,3,7 or with increasing size of the surfactant micelle.2,3,6,7 The latter may be varied either by varying the length of the hydrophobic and/or hydrophilic parts of the surfactant, or, in certain cases, by varying the temperature. The mixtures studied so far have also displayed a markedly uneven partitioning of the solvent between the two separating phases, so that the surfactant-rich phase was always more concentrated than the polymer-rich phase.3-7 In order to rationalize the phase behavior, most of the previous investigators draw the analogy between polymer/surfactant segregation and the segregation occurring in mixtures of flexible polymers in a common solvent.2-6 According to our present understanding, the phase behavior of the latter type of mixture is governed by the effective short-range pair interactions (as expressed by the χ-parameters of the Flory-Huggins theory11), and segregation may be caused by either an effective repulsion between the unlike polymers11,12 or a sufficiently large difference in their interactions with the solvent.13 Indications that the polymer-surfactant (headgroup) interactions are indeed important were found in our preliminary study,2 where we found less segregation for chemically similar couples. Clegg et al.,7 however, focused in their analysis on the difference in shape between the polymer and the surfactant micelle, in considering the latter to be analogous to a colloidal particle. They interpreted the polymer/micelle segregation in terms of the polymer depletion mechanism, which has been found, theoretically14-17 and experimentally,18-20 to give rise to a segregative phase separation in mixtures of mixtures of colloidal particles with nonadsorbing polymers. It is notable that the © 1996 American Chemical Society

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Piculell et al.

driving force for this type of segregation is entropic rather than enthalpic; it is caused by the “depletion layer” of lower polymer segment concentration that develops outside the surface of a nonadsorbing particle. The theory, using the polymer radius of gyration as an estimate of the thickness of the depletion layer, predicted much stronger segregation than was observed experimentally by Clegg et al.; 7 in contrast to the experimental results, a phase separation was predicted to occur at polymer concentrations much below the overlap concentration. One of the purposes of the present study is to explore in more detail the role of the short-range interactions in the phase behavior of polymer/surfactant mixtures. We have therefore selected for study combinations of polymer and surfactant where the surfactant headgroup is either chemically similar to or different from the repeating unit of the polymer. The polymers are dextran and PEO, and the surfactants are C12E8, C12E5, and n-octyl-β-D-glucopyranoside (C8G1). The choice of these particular varieties of alkyl oligo(ehylene oxide) and alkylglucoside surfactants was dictated by the second purpose of our study, which is to study in more detail the role of micellar size in determining the phase behavior. C12E5 is well-known to form large prolate micelles that grow rapidly in size with increasing temperature.21,22 In contrast, the C12E8 micelles are more nearly spherical and constant in size over a large temperature interval, up to ca. 40-50 °C.21-24 The C8G1 micelles, although nonspherical, are also rather constant in size at temperatures below ca. 40 °C.25 Experimental Section Materials. Dextran T70 (from Pharmacia, Uppsala, Sweden), with a molecular weight of Mw ) 70 000 (from dextran calibrated GPC and from light scattering in our laboratory) and with Mw/Mn ) 1.1 (from dextran calibrated GPC), was purified by ultrafiltration and then freeze-dried. In the experimental phase diagrams, no corrections for the water content in the freeze-dried dextran were made. The latter was estimated to 2-3% from drying to constant weight in Vacuo. PEO with a molecular weight of 40 000 (as confirmed by light scattering in our laboratory) was from Serva, Heidelberg, Germany, and was used as received. The surfactants penta(ethylene oxide) dodecyl ether (C12E5) and octa(ethylene oxide) dodecyl ether (C12E8) were of high quality from Nikko Chemical Co., Japan, and C8G1 was from Sigma Chemical Co., St. Louis, MO. All surfactants were used without further purification. The water used was of Millipore quality. Polymer and surfactants concentrations are given in weight percent (%) throughout. Methods. Binodals were obtained at various temperatures from cloud point measurements. Samples were prepared in the two-phase region (turbid samples) by mixing suitable stock solutions in a jacketed glass beaker connected to a thermostated (refrigerated) circulator with a temperature stability of (0.1 °C. Water was then added in small portions until the samples reached the one-phase region. A sample was regarded as monophasic when it was completely clear (without stirring) visually. Tie lines for dextran/C12E5 and dextran/C12E8 were obtained at 10.2 °C by the following procedure. Samples were prepared as for the cloud-point measurements. After 3 h in the circulator, they were shaken vigorously and left in the circulator to achieve macroscopic phase separation. After 3 days, the dextran/C12E8 mixtures had separated into clear top and bottom phases, whereas some of the surfactant-rich top phases of the dextran/ C12E5 mixtures (mainly in the more concentrated samples) were still cloudy, owing to their higher viscosity. The dextran/C12E5 samples were therefore centrifuged (3000 rpm) for 30 min at

Figure 1. Ternary phase diagrams (compositions in weight percent) at 10.2 °C for mixtures of dextran T70 with C12E5 (a, top) and C12E8 (b, bottom). Tie lines connect equilibrium phases of indicated compositions (b) separated from samples of indicated total compositions (+). The top parts of the phase boundaries are based on cloud-point measurements.

10 ( 0.5 °C and then immersed again in the circulator for 2 more days. After this treatment, all top and bottom phases were completely clear, and they were also found to be optically isotropic. (At higher concentrations, optical birefringence was observed in some mixtures involving C12E5.) The phases were collected separately and diluted as appropriate for the concentration determinations. The dextran content was determined by optical rotation in a digital polarimeter DIP-360, Jasco International Co., Ltd., Japan, at 435 nm (samples diluted 4-10 times). The surfactant content was obtained from measurements of the refractive index in a differential refractometer 2142 LKB, Bromma, Sweden, by using calibration curves determined for the individual solutes and subtracting the contribution from dextran. Prior to these measurements, the samples were diluted to a total solute concentration of e0.4%, where measurements had shown that the contributions to the refractive index from the different solutes were additive. Results and Discussion Dextran/C12E8, C12E5. Figure 1 shows phase diagrams, with tie lines, for mixtures of dextran T70 with C12E5 and C12E8 at 10 °C. This temperature is far below the lower consolute curves of the binary surfactant/water mixtures, which display minima around 80 and 30 °C for C12E8 26 and C12E5,27 respectively. As expected, and as demonstrated in our earlier study,2 the twophase area is much larger in the system containing the largest surfactant micelle (C12E5). This system also features the markedly uneven distribution of solvent (cf. the sloping tie lines in Figure 1a), noted in previous investigations of segregating polymer/surfactant mixtures.3-7 Interestingly, the difference in

Segregation in Polymer and Micelle Mixtures

Figure 2. Phase boundaries (compositions in weight percent) from cloud-point measurements for mixtures of dextran T70 with (from top to bottom) C12E5 at 25 °C, C12E5 at 10 °C, C12E8 at 10 °C, and C12E8 at 25 °C.

water content is much smaller with the smaller C12E8 micelles (cf. the nearly horizontal tie lines in Figure 1b). This suggests that one important contribution to the observed uneven solvent distribution may be a large molecular weight of the micelle. Assuming an aggregation number in the range of 80-100,23,24 we arrive at a molecular weight in the range of 43 000-54 000 already for the rather small C12E8 micelles. This is quite comparable to the molecular weight of dextran T70. The aggregation number of the C12E5 micelles is not accurately known; it is so large that it is difficult to measure with the usual fluorescence techniques.28 In Figure 2, we show the effect of temperature in the lowtemperature range (e25 °C) on the phase boundaries of the dextran/C12Em mixtures. For the mixture with C12E5, where significant micellar growth occurs on increasing the temperature, the two-phase area increases on going from 10 to 25 °C. For the mixture with C12E8, on the other hand, there is little variation of the micellar size in this temperature range, and here the twophase area actually undergoes a small, but significant, decrease on increasing the temperature. This result confirms our earlier conclusion, based on measurement on similar systems, regarding the importance of micellar growth for polymer/surfactant segregation.2 We note that the segregation with dextran T70 is stronger for both C12E8 and C12E5 than what Clegg et al. found for mixtures of the same dextran with C10E6 at room temperature. This trend is expected, in view of the smaller micellar size of the latter surfactant. PEO/C12E8, C12E5. Binodals for mixtures of PEO 40000 with C12E8 and C12E5 at a range of different temperatures below the lower consolute curves of the respective surfactant/water mixtures are shown in Figure 3. The patterns from Figure 2 are clearly apparent also when dextran is changed for PEO: The segregation is stronger with C12E5 and increases monotonically with increasing temperature. In contrast, the (much weaker) segregation with C12E8 decreases with increasing temperature in the low-temperature range (10-25 °C). Interestingly, however, the latter trend is broken at higher temperatures, where there is known to be significant micellar growth; here, the twophase area increases with increasing temperature, just as in the mixtures with C12E5. The rather substantial growth of the twophase area already between 25 and 40 °C is notable, since literature data show no evidence of dramatic micellar growth of C12E8 in this region.22-24 It should be remembered, however, that all the latter data refer to measurements at much higher water contents and in the absence of polymer. Possibly, the

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Figure 3. Phase boundaries (compositions in weight percent) from cloud-point measurements for mixtures of PEO 40 000 with (from top to bottom) C12E5 (dashed lines) at 29, 25, 20, and 10 °C and C12E8 (solid lines) at 70, 55, 40, 10, and 25 °C.

Figure 4. Phase boundaries (compositions in weight percent) from cloud-point measurements for mixtures of C8G1 with (from top to bottom) PEO 40 000 at 10 °C, PEO at 25 °C, dextran T70 at 10 °C, and dextran T70 at 25 °C.

micellar growth starts at lower temperatures in the more concentrated mixtures considered here. Wormuth3 found a monotonically increasing segregation with increasing temperature in mixtures of PEO 20 000 with C8E4 in the range of 0-40 °C, i.e., the same trend that we find in regions where there is significant micellar growth. Compared at the same temperatures, the two-phase areas he found for PEO/ C8E4 are larger than those for PEO/C12E8, but smaller than those for PEO/C12E5 in Figure 3. The differences are so large that they should not be due to the fact that Wormuth used a PEO which was shorter than ours. PEO, Dextran/C8G1. In Figure 4 we show binodals for the two polymers, PEO 40 000 and dextran T70, mixed with C8G1 at 10 and 25 °C. For both polymers, the segregation with C8G1 decreases with increasing temperature. The effect is quite small for the mixture with dextran, but it is significant: A sample that was completely clear (monophasic) at 25 °C became turbid on cooling. Octylglucoside micelles have been found to grow quite slowly with increasing temperature below 40 °C.25 The temperature trends in Figure 4 are thus consistent with our findings for C12E8, i.e., that the two-phase area decreases with increasing temperature when there is no or little micellar growth. The effect of temperature is seen to be much larger for PEO than for dextran. This could reflect differences in the temperature dependence of the short-range interaction parameters (polymer/surfactant or polymer/water) for the two polymers. However, one should

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Figure 5. Comparison of phase boundaries (compositions in weight percent) for all studied polymer/surfactant couples at 10 °C with (from top to bottom) PEO 40000/C12E5, dextran T70/C12E5, PEO 40000/C8G1, dextran T70/C12E8, dextran T70/C8G1, and PEO 40000/C12E8.

also consider the fact that the phase separation occurs at much lower water contents for dextran than for PEO. As pointed out above, there may be larger micellar growth with increasing temperature in the more concentrated systems. This means that the “normal” temperature trend (decreasing two-phase area with increasing temperature) might be partly counteracted by a significant micellar growth in the mixture that phase separates at higher concentrations. Another factor to take into consideration is variations in the concentration of monomeric octylglucoside. Unlike the C12Em surfactants, C8G1 has a quite high critical micelle concentration (cmc), and the concentration of monomeric surfactant is therefore not negligible in the mixtures investigated here. From the data of Kamayama and Tagaki25 we find that the cmc of octylglucoside decreases from 0.92% at 10 °C to 0.74% at 25 °C. Assuming that the monomer concentration in our mixtures is roughly equal to the cmc, we conclude that the increase in temperature should lead to a corresponding increase in the micellar concentration, at a given total concentration of surfactant. This effect, in addition to possible micellar growth, should favor a growth of the twophase area with increasing temperature. Effects of Headgroup-Polymer Interactions. Figure 5 compares the binodals for all the investigated polymer/surfactant couples at a single temperature (10 °C), far below the lower consolute curves of the C12Em /water mixtures. For the mixtures involving small micelles of roughly constant size (C12E8 and C8G1), there is a clear trend that couples in which the surfactant headgroups and polymer repeating units are chemically similar (PEO/C12E8 and dextran/C8G1) are much more miscible than couples with chemically different hydrophilic units (dextran/ C12E8 and PEO/C8G1). This is the expected result, if shortrange headgroup/polymer interactions are important factors in determining the extent of the segregation. Surprisingly, the mixtures with C12E5 show the opposite trend, in that the miscibility is actually smallest for the chemically related PEO/ C12E5 couplesdespite the higher molecular weight of the dextran polymer. In view of the results obtained for the other polymer/surfactant pairs, it seems unlikely that the larger segregation for PEO/ C12E5 than for dextran/C12E5 should be caused by more unfavorable polymer/surfactant interactions for the former couple. General considerations immediately suggest two other possible explanations: the C12E5 micelles could be larger in the mixture with PEO than in the mixture with dextran, or the difference in the effective interactions of the two solutes (polymer and surfactant) with the solvent could be larger. Both of these mechanisms should lead to a more asymmetric

Piculell et al. partitioning of the solvent between the surfactant-rich and the polymer-rich phases in the mixture with PEO. Approximate determinations of the tie lines, through measurements of phase volumes of separated phases, suggest that this is indeed the case. With regard to the possible role of solvency, we note that in segregating PEO/dextran mixtures, the PEO-rich phase is generally more dilute than the dextran-rich phase in the temperature range (room temperature and below) considered here.8,29 This fact indicates that in this temperature range (the trend is reversed at high temperatures29), water is a better solvent for PEO than for dextran. Since water is a rather poor solvent for the C12E5 micelles (cf. the demixing that occurs at ca. 30 °C), it could be argued that the effective solute/solvent interactions are actually more different for C12E5 and PEO than for C12E5 and dextran. The evidence is admittedly quite indirect, however. Another factor that should be important for the fairly dilute phase separation with C12E5 is the size of the polymer molecule. From tabulated Mark-Houwink-Sakurada relationships30 we deduce that the intrinsic viscosities at 25 °C should be roughly 0.40 and 0.25 mL/g for PEO 40 000 and dextran T70, respectively. This means that the average size of a random coil of PEO 40 000, despite its lower molecular weight, is actually larger than that of dextran T70. The larger size increases the probability of (unfavorable) polymer/micelle contacts in the random mixture and, hence, the tendency toward phase separation. At this stage we cannot exclude or confirm any of the possible explanations of the larger segregation for PEO/C12E5 than for dextran/C12E5. Measurements of the micellar sizes in the segregating mixtures should be informative, but such measurements are difficult at the high surfactant concentrations required to obtain phase separation.28 Conclusions Our study supports the conclusions of previous studies, that micellar size is an important factor in determining the extent of the two-phase area in segregating polymer/surfactant solutions. Thus, an increase in micellar size with increasing temperature, such as those for C12E5 and for C12E8 at sufficiently high temperatures, resulted in a larger two-phase area. In contrast, for systems and temperature regions where the micellar size is expected to change little with temperature, the miscibility increased with increasing temperature. Comparisons of the phase behavior of different combinations of surfactant and polymer indicate that short-range interactions are important for the phase behavior. In most cases, the exception being mixtures of C12E5 with dextran and with PEO, we found that a chemical similarity between the polymer and the surfactant headgroup increased the miscibility. This interpretation is also supported by experiments from Albertsson’s laboratory, showing that micelles of the nonionic surfactant Triton-X-100, which has oligo (ethylene oxide) headgroups, partitions to the PEO-rich phase in aqueous two-phase systems based on dextran and PEO.8 Our results on C12E8/dextran demonstrate that the surfactantrich phase is not necessarily much more concentrated than the polymer-rich phase in a segregating polymer/surfactant mixture. The small size of the C12E8 micelle should contribute to the relatively large water content in the surfactant-rich phase in the dextran mixture, but the solvency could also be important. Since the surfactant/water interactions are important factors in determining micellar size, it should generally be difficult to separate effects of micellar solvency and size on the phase behavior in mixtures with polymers.

Segregation in Polymer and Micelle Mixtures Although there are obvious analogies between polymer/ polymer and polymer/surfactant mixtures, there are also important differences, which should not be forgotten. The conformational degrees of freedom do not depend on the overall concentration in the same way for a (spherical) micelle as for a flexible polymer. A rodlike micelle might be modeled as a semiflexible polymer, but one must still consider the fact that it is much thicker than a normal flexible polymer. A comparison of experimental results on polymer/polymer vs polymer/surfactant mixtures underscores the differences. For instance, the two-phase area at room temperature is much larger for dextran/ PEO mixtures8 than for the analogous dextran/C12E8 mixtures, even for PEO polymers with a much lower molecular weight than the C12E8 micelles. We ascribe this difference to the fact that the effective volume of a swollen polymer coil is larger than that of a compact micelle. This means that the number of segment/segment contacts should be larger in polymer/polymer mixtures than in mixtures of a polymer with a nonionic surfactant. Thus, although models (such as the Flory-Huggins model) of mixtures of flexible polymers may be useful in qualitative discussions, they should not be expected to yield quantitatively correct descriptions of polymer/surfactant segregation. On the other hand, the entropic depletion model7 does not seem to offer a satisfactory alternative. For one thing, shortrange interactions must be included in the model in order to capture important trends found experimentally. This is clearly illustrated by the findings in the present work and was also pointed out by Clegg et al. in their study.7 We note, however, the neglect of short-range interactions is not expected to give rise to such discrepancies between experiment and model predictions as was encountered in the latter study. Short-range interactions generally favor contacts between like molecules, and they are therefore expected to increase, rather than decrease, the tendency for segregation. In our opinion, the most serious problem with the depletion model in the present context is the fact that spherical micelles are normally much smaller (by up to 1 order of magnitude in reference 7) than the radius of gyration of the polymer. Such small objects should not be strongly excluded from the polymer domain. The depletion effect is thus strongly exaggerated when the polymer radius of gyration (or the correlation length ξ in semidilute solutions16) is used as an estimate of the distance of closest approach between polymer and micelle. The real distance of closest approach is difficult to estimate, but it is anticipated that it should also depend on the persistence length of the polymer, when this length is not negligible compared to the size of the micelle. In short, the most difficult problem in the quantitative modeling of polymer/surfactant mixtures seems to be the “spaghetti-and-meatballs” character of the system: The dimen-

J. Phys. Chem., Vol. 100, No. 9, 1996 3679 sions of the surfactant micelle are normally small compared to the radius of gyration of the polymer, but they are large compared to the polymer thickness. Acknowledgment. We are indebted to Drs. Ilias Iliopoulos, Svante Nilsson, and Per Linse for several rewarding discussions and to Dr. Christer Viebke for performing the molecular weight determinations by light scattering. This work was supported by grants from the Swedish National Board for Industrial and Technical Development (NUTEK) and from the Swedish Natural Science Research Council (NFR). References and Notes (1) Interaction of Surfactants with Polymers and Proteins, Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (2) Piculell, L.; Lindman, B. AdV. Colloid Interface Sci. 1992, 41, 149. (3) Wormuth, K. R. Langmuir 1991, 7, 1622. (4) Thalberg, K.; Lindman, B.; Karlstro¨m, G. J. Phys. Chem. 2091, 95, 6004. (5) Lindman, B.; Thalberg, K. In ref 1; p 203. (6) Thalberg, K.; Lindman, B. Colloids Surf. A 1993, 76, 283. (7) Clegg, S. M.; Williams, P. A.; Warren, P.; Robb, I. D. Langmuir 1994, 10, 3390. (8) Albertsson, P.-Å. Partition of Cell Particles and Macromolecules, 3d ed.; Wiley-Interscience: New York, 1986. (9) Morris, E. R. In Food Gels, Harris, P., Ed.; Elsevier Applied Science: London, 1990; p 291. (10) Svensson, M.; Linse, P.; Tjerneld, F. Macromolecules 1995, 28, 3597. (11) Flory, P. J. Principles of Polymer Chemistry, 13th ed.; Cornell University Press: Ithaca, NY, 1953. (12) Scott, R. L. J. Chem. Phys. 1949, 17, 279. (13) Zeman, L.; Patterson, D. Macromolecules 1972, 5, 513. (14) Asakura, S.; Oosawa, F. J. Polym. Sci. 1958, 33, 183. (15) Vrij, A. Pure Appl. Chem. 1976, 48, 471. (16) Joanny, J. F.; Leibler, L.; de Gennes, P. G. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1073. (17) Lekkerkerker, H. N. W.; Poon, W. C.-K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (18) Sperry, P. R.; Hopfenberg, H. B.; Thomas, N. L. J. Colloid Interface Sci. 1981, 82, 62. (19) de Hek, H.; Vrij, A. J. Colloid Interface Sci. 1981, 84, 409. (20) Vincent, B.; Edwards, J.; Emmett, S.; Croot, R. Colloid Surf. 1988, 31, 267. (21) Lindman, B.; Jonstro¨mer, M. In Physics of Amphiphilic Layers, Meunier, J., Langevin, D., Boccara, N., Eds.; Springer-Verlag: Berlin, Heidelberg, 1987; p 235. (22) Jonstro¨mer, M.; Jo¨nsson, B.; Lindman, B. J. Phys. Chem. 1991, 95, 3293. (23) Zana, R.; Weill, C. J. Phys. Lett. 1985, 46, L-953. (24) Anthony, O.; Zana, R. Langmuir 1994, 10, 4048. (25) Kameyama, K.; Takagi T. J. Colloid Interface Sci. 1990, 137, 1. (26) Shinoda, K. J. Colloid Interface Sci. 1970, 34, 278. (27) Strey, R.; Schoma¨cker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253. (28) Hansson, P.; Almgren, M. Personal communication. (29) Sjo¨berg, Å.; Karlstro¨m, G. Macromolecules 1989, 22, 1325. (30) Polymer Handbook, 3d ed.; Brandrup, J., Immergut, E. H., Eds.; Wiley, New York, 1989.

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