Origins of Anomalous Micellization in Diblock Copolymer Solutions

interval just above the cmt. We propose that anomalous micellization is due to the incipient phase separation of small amounts of polystyrene homopoly...
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Langmuir 2003, 19, 2103-2109

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Origins of Anomalous Micellization in Diblock Copolymer Solutions Timothy P. Lodge,* Joona Bang, Kenneth J. Hanley, James Krocak, Stephanie Dahlquist, Brijesh Sujan, and Joseph Ott Department of Chemistry and Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received November 20, 2002. In Final Form: December 17, 2002 The phenomenon of “anomalous” micellization is investigated in dilute solutions of two nearly symmetric poly(styrene-b-isoprene) diblock copolymers, via dynamic light scattering. In two polystyrene-selective solvents, diethyl phthalate and dimethyl phthalate, the critical micelle temperatures (cmt) are clearly determined by rather abrupt increases in the hydrodynamic radius and scattered intensity upon cooling; this corresponds to “normal” micellization. In contrast, for the same polymers dissolved in two polyisopreneselective solvents, tetradecane and squalane, anomalous micellization was consistently observed: the hydrodynamic radius exceeded 1000 Å and the intensity was unusually large, over a modest temperature interval just above the cmt. We propose that anomalous micellization is due to the incipient phase separation of small amounts of polystyrene homopolymer, resulting from incomplete crossover during the sequential anionic polymerization of styrene and isoprene. In one sample, the presence of homopolymer (ca. 1 wt % of copolymer) was confirmed by chromatography, and removal of this impurity eliminated the anomalous micellization. Addition of similar amounts of polyisoprene homopolymer to the same sample induced anomalous micellization in the polystyrene-selective solvents, with the onset of the effect corresponding to the cloud point for the polyisoprene homopolymer. These observations support the proposed hypothesis; the extent to which this hypothesis may extend to previous reports of anomalous micellization is discussed.

Introduction The phenomenon of micellization in block copolymer solutions has been a subject of considerable interest for over 40 years.1,2 A great deal is now known about the various self-assembled structures that can be formed and the factors that influence the choice of structure and the location of the critical micelle concentration (cmc) and critical micelle temperature (cmt). An interesting phenomenon associated with the micellization process, and especially in the context of the cmt, has been termed “anomalous micellization”.1,3-27 The details of this phenomenon do vary from system to system, and the term * To whom correspondence should be addressed. E-mail: lodge@ chem.umn.edu. (1) Tuzar, Z.; Kratochvil, P. In Surface and Colloid Science; Matijevic, E., Ed.; Plenum Press: New York, 1993; Vol. 15, p 1. (2) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: Oxford, 1998. (3) Lally, T. P.; Price, C. Polymer 1974, 15, 325. (4) Tuzar, Z.; Sikora, A.; Petrus, V.; Kratochvil, P. Makromol. Chem. 1977, 178, 2743. (5) Mandema, W.; Zeldenrust, H.; Emeis, C. A. Makromol. Chem. 1979, 180, 1521. (6) Mandema, W.; Emeis, C. A.; Zeldenrust, H. Makromol. Chem. 1979, 180, 2163. (7) Canham, P. A.; Lally, T. P.; Price, C.; Stubbersfield, R. B. J. Chem. Soc., Faraday Trans. 1 1980, 76, 1857. (8) Selb, J.; Gallot, Y. Makromol. Chem. 1980, 181, 809. (9) Ahmad, N.; Kaleem, M.; Noor, S. Colloid Polym. Sci. 1983, 261, 898. (10) Sikora, A.; Tuzar, Z. Makromol. Chem. 1983, 184, 2049. (11) Bednar, B.; Devaty, J.; Koupalova, B.; Kralicek, J.; Tuzar, Z. Polymer 1984, 25, 1178. (12) Peng, X.; Zhou, Z. Huaxue Xuebao 1986, 44, 613. (13) Price, C.; Briggs, N.; Quintana, J. R.; Stubbersfield, R. B.; Robb, I. Polymer Commun. 1986, 27, 292. (14) Price, C.; Chan, E. K. M.; Hudd, A. L.; Stubbersfield, R. B. Polymer Commun. 1986, 27, 196. (15) Duval, M.; Picot, C. Polymer 1987, 28, 793. (16) Khan, T. N.; Mobbs, R. H.; Price, C.; Quintana, J. R.; Stubbersfield, R. B. Eur. Polym. J. 1987, 23, 191. (17) Zhou, Z.; Chu, B. Macromolecules 1987, 20, 3089. (18) Zhou, Z.; Chu, B. Macromolecules 1988, 21, 2548.

has not been universally adopted, but the general features of anomalous micellization may be summarized as follows.1,2 Some dilute copolymer solutions show three regimes of behavior as a function of temperature: spherical micelles, single chains, and an intermediate anomalous regime. In this intermediate regime, the intensity of scattered light is very high and shows a pronounced angular dependence; in some cases the solution becomes visibly turbid. Similarly, hydrodynamic radii extracted from dynamic light scattering measurements often exceed 1000 Å, in contrast to the values typically associated with normal micelles (ca. 100-300 Å) or single chains (tens of angstroms). The anomalous regime extends over about 10-40 °C or so in temperature. Whether the single-chain region is accessed at high temperature or low temperature depends on the system employed; micellization usually occurs on cooling in organic solvents but on heating for poly(ethylene oxide)-containing copolymers in water. Many explanations have been proposed over the years for the origin(s) of anomalous micellization.1,2 Some may be viewed as “intrinsic” to the micellization process, for example, the formation of particular large assemblies such as hollow spherical micelles25,27 or wormlike micelles,7,14 (19) Tuzar, Z.; Stehlichek, J.; Konak, C.; Lednicky, F. Makromol. Chem. 1988, 189, 221. (20) Tuzar, Z. Macromol. Rep. 1992, A29, 173. (21) Tuzar, Z.; Kratochvil, P.; Prochazka, K.; Munk, P. Collect. Czech. Chem. Commun. 1993, 58, 2362. (22) Chu, B.; Zhou, Z.; Wu, G. J. Non-Cryst. Solids 1994, 172-174, 1094. (23) Dubrovina, L. V.; Bragina, T. P.; Makarova, L. I.; Filimonova, L. V.; Pavlova, S. A.; Zhdanov, A. A. Vysokomol. Soedin., Ser. A Ser. B 1996, 38, 1419. (24) Grubisic-Gallot, Z.; Sedlacek, J.; Gallot, Y. J. Liq. Chromatogr. Relat. Technol. 1998, 21, 2459. (25) Iyama, K.; Nose, T. Polymer 1998, 39, 651. (26) Fukumine, Y.; Inomata, K.; Takano, A.; Nose, T. Polymer 2000, 41, 5367. (27) Nose, T.; Numasawa, N. Comput. Theor. Polym. Sci. 2001, 11, 167.

10.1021/la0268808 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/07/2003

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or the presence of long-range correlated concentration fluctuations.13 Other explanations are “extrinsic” in nature, for example, that the origin lies in the phase separation or premicellization of some kind of impurity.4,17,18,22,28,29 Various candidate impurities have been proposed, including compositionally heterogeneous copolymers and homopolymers corresponding to one of the blocks. Interestingly, a significant fraction of the papers on the topic have not really advocated any particular explanation. Although there is no compelling reason to expect a single explanation to account for all the experimental observations, it would certainly be more satisfying if there were fewer explanations than systems examined, and in particular if one explanation could account for the majority of the particular cases. Toward this end, the work of Tuzar and co-workers21 and Chu and co-workers17,18,22 is particularly noteworthy, as they have shown that it is possible to filter out the anomalous micelles and thereby make the effect go away. These results argue strongly against any intrinsic explanation, and both of these groups conclude that impurities are essential features. The precise nature or origin of these impurities has not been established, however. In this paper, we examine the micellization of symmetric poly(styrene-b-isoprene) (PS-PI) diblock copolymers in four solvents: diethyl phthalate and dimethyl phthalate, both selective for PS, and tetradecane and squalane, both selective for PI. In the PS-selective solvents, only “normal” micellization is observed, whereas in the PI-selective solvents anomalous micellization is consistently seen. We demonstrate conclusively that anomalous micellization is a result of incipient phase separation of trace amounts of PS homopolymer, which are present due to incomplete crossover to the second block during the sequential polymerization of styrene and isoprene. We show that the effect can be made to disappear by removing the PS homopolymer, and it can be made to appear in PS-selective solvents by adding small amounts of PI homopolymer. We also discuss the extent to which this explanation can be invoked to rationalize the many previous observations. This situation is complicated in part by the fact that the majority of systems in which the effect has been observed involve ABA triblock copolymers, rather than diblocks. In this case, the “natural” impurities could include diblocks as well as homopolymers and should also depend on the mode of polymerization (sequential addition, diblock coupling, or difunctional initiation), which is often not completely specified. Nevertheless, we propose that anomalous micellization is always the result of particular impurities, such as homopolymers in the case of diblocks or homopolymers and diblocks in the case of triblocks; conversely, we suspect that statistical compositional heterogeneity is unlikely to be sufficient in most cases. Experimental Section Samples and Solutions. Two PS-PI diblock copolymers, designated SI(15-15), with block molecular weights of 1.5 × 104 and 1.5 × 104, respectively, and SI(8-7), with block molecular weights of 8.0 × 104 and 7.0 × 104, respectively, were synthesized by living anionic polymerization using standard procedures.30 Cyclohexane was used as a solvent to promote 4,1-addition of PI. The number-average molecular weight and the polydispersity (Mw/Mn ≈ 1.02) were determined by size exclusion chromatog(28) Tuzar, Z.; Kratochvil, P. Makromol. Chem. 1973, 170, 177. (29) Tuzar, Z.; Bahadur, P.; Kratochvil, P. Makromol. Chem. 1981, 182, 1751. (30) Lodge, T. P.; Pudil, B.; Hanley, K. J. Macromolecules 2002, 35, 4707.

Lodge et al. raphy (SEC), and the block composition and the mole percent of 4,1-addition of the PI block (ca. 94%) were determined by 1H NMR. Assuming additivity of volumes and densities of 1.047 g/mL (PS) and 0.913 g/mL (PI), the PS volume fractions were calculated to be fPS ) 0.47 and 0.49 for SI(15-15) and SI(8-7), respectively. Diethyl phthalate (DEP) and dimethyl phthalate (DMP) were used as PS-selective solvents, and n-tetradecane and squalane were used as PI-selective solvents. The solvents were obtained from Aldrich Chemical Co., and all but squalane were purified by vacuum distillation (150 °C, 3 mmHg). Polymer solutions were prepared gravimetrically, with the aid of methylene chloride as a cosolvent. Methylene chloride was removed from the solution with a nitrogen purge while stirring at room temperature for a few days, until the sample weight indicated that a few milligrams of solvent had also been removed. Concentrations were converted to the polymer volume fractions based on additivity of volumes and densities of 1.118, 1.16, 0.763, and 0.810 g/mL for DEP, DMP, tetradecane, and squalane, respectively. For all solutions, the polymer volume fraction φ was maintained at ca. 0.01 to diminish intermicellar interactions. Light Scattering. The sample solutions were passed through 0.2 µm filters (Millipore) into 0.25 in. diameter optical glass tubes. The tube was flame-sealed under a vacuum to prevent oxidative degradation and dust contamination. The samples were investigated using a home-built photometer equipped with a electrically heated silicon oil index-matching bath, a Brookhaven BIDS photomultiplier, and a Lexel Ar+ laser operating at 488 nm. Dynamic light scattering measurements were made with the assistance of a Brookhaven BI-9000 correlator. Samples were annealed at the set temperature for at least 5 min before intensity autocorrelation functions, g(2)(t), were recorded at various temperatures. At each selected temperature, measurements were usually made at a minimum of three scattering angles from 50° to 130°. For solutions containing primarily spherical micelles or single chains, the observed behavior is dominated by a single decay mode, and the correlation functions are well described with a single-exponential decay. In this case, the field correlation function, g(1)(t), is

g(1)(t) ) exp(-Γt) ) exp(-Dq2t)

(1)

where Γ is the decay rate, D is the diffusion coefficient, and q is the scattering vector (q ) 4π/λ sin(θ/2), where λ is the wavelength of the light in the medium and θ is the scattering angle). The field correlation function is related to the intensity correlation function by

g(2)(t) ) 1 + β|g(1)(t)|2

(2)

where β is an instrument constant between 0 and 1. Using the Stokes-Einstein relation

D)

kT 6πηsRh

(3)

the hydrodynamic radius Rh can be estimated with knowledge of the solvent viscosity, ηs. However, within the anomalous micellization regime the correlation functions often (but not always) exhibit two decay modes (fast and slow modes). Then, the field correlation function can be well described by a sum of two exponentials:

g(1)(t) ) A1exp(-Γ1t) + A2exp(-Γ2t) ) A1exp(-D1q2t) + A2exp(-D2q2t) (4) The fits using eqs 1 and 3 were undertaken with a standard nonlinear regression program; fits were deemed satisfactory when the resulting χ2 was less than 10-6. The double exponential fit was used for SI(15-15) in tetradecane and for SI(8-7) plus PI-11 in DEP (vide infra).

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Results The cmt is readily identified by either the scattered intensity or the hydrodynamic radius. The latter quantity is shown as a function of temperature in Figure 1 for two copolymers in two PS-selective solvents: SI(15-15) in DMP in Figure 1a and SI(8-7) in DMP and DEP in Figure 1b. In all cases, Rh is approximately independent of T at low T, with a value typical of spherical micelles, before dropping abruptly over a few degrees to a value typical of a single chain. The cmt for SI(8-7) is about 70 °C higher in DMP than DEP, which is a direct reflection of the fact that DMP is a more selective solvent for PS.30 Likewise, the cmt for SI(15-15) in DMP is about 40 °C higher than for SI(8-7) in the same solvent, due to the higher M. The Rh values for SI(15-15) fall in the vicinity of 200 Å, whereas for SI(8-7) they are about 120 Å. This difference is also primarily attributable to the difference in M. The scattered intensities for these solutions consistently indicate the same behavior, with equivalent values of the cmt. Examples are provided for SI(8-7) in DMP and DEP in Figure 1c. All of these features of the cmt are typical of normal micellization in block copolymers.1,2 The analogous plots for the same two polymers in two PI-selective solvents, tetradecane and squalane, are shown in Figure 2a,b. In all four cases, the T dependence of Rh is markedly different from that shown in Figure 1; between the low T region associated with compact micelles and the high T region characteristic of single chains, there appears an interval of about 30 °C in width where Rh exceeds 1000 Å. The scattered intensities also show a substantial increase over the same temperature region where Rh is anomalously large; Figure 1c includes the data for SI(8-7) in tetradecane as an example. These, in turn, are both distinctive features of anomalous micellization, as has been demonstrated for many systems in the past.1,2 Note that the values of Rh both below and above the anomalous region are equivalent to those in the PS-selective solvents shown in Figure 1. Note also that for both polymers the anomalous region occurs at higher temperatures in squalane than in tetradecane, which reflects the fact that squalane is the more PI-selective.31 Finally, this anomalous behavior is observed both on cooling slowly from high temperature and on heating slowly from low temperature; that is, it is fully reversible. These results demonstrate clearly that anomalous micellization is not an inherent feature of the micellization process, nor is it an intrinsic property of a particular block copolymer. Because the two copolymers examined are essentially symmetric, we may further conclude that anomalous micellization has nothing to do with preferred curvature at the PS-PI interface. Rather, the essential feature is connected to whether the solvent is PS-selective or PI-selective. It has previously been suggested that anomalous micellization is due to phase separation as a result of compositional heterogeneity, that is, chains that contain more than the average amount of the insoluble component.17,18,22 However, in this case there is no particular reason the synthetic procedure should produce more PS-rich copolymers than PI-rich copolymers. We propose, rather, that the asymmetry with respect to solvent selectivity is due to the asymmetry in the synthesis, namely, that PS blocks are polymerized first. Consequently, if the crossover to the PI block is anything less than 100% efficient, there will be PS homopolymers present in the sample. Conversely, although there are mechanisms by which PI homopolymers could also be (31) Lai, C.; Russel, W. B.; Register, R. A. Macromolecules 2002, 35, 841.

Figure 1. Micellization in styrene-selective solvents: (a) hydrodynamic radius versus temperature for SI(15-15) in DMP; (b) hydrodynamic radius versus temperature for SI(8-7) in DMP and DEP; (c) scattered intensity (normalized to the value at low temperature) at a scattering angle of 90° versus temperature for SI(8-7) in DMP, DEP, and the isoprene-selective solvent tetradecane.

produced (see Discussion), they are less likely in this system. When the copolymer sample is dissolved in PIselective solvents, the residual PS homopolymer will have a tendency to phase separate prior to the cmt (i.e., at higher

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Figure 3. Normalized SEC chromatograms for SI(15-15) before and after fractionation.

Figure 2. Micellization in isoprene-selective solvents: (a) hydrodynamic radius versus temperature for SI(15-15) in tetradecane and squalane; (b) hydrodynamic radius versus temperature for SI(8-7) in tetradecane and squalane.

temperature). The anomalously large values of Rh and scattered intensity reflect some kind of large assemblies, which we propose are emulsion-like droplets rich in PS homopolymer, that are partially stabilized by the copolymers. Once the “real” cmt is reached, that is, the temperature at which the pure copolymers would micellize, the copolymers can easily solubilize the PS homopolymers in the cores of normal micelles. Thus the trace amount of homopolymer only has a discernible effect on the solution properties over a narrow interval of temperature above the cmt. Note that it is quite natural for phase separation of the homopolymer to occur just a few degrees prior to the micellization of a diblock containing a similar length unfavorable block; the covalent attachment of a block under good solvent conditions should stabilize the singlechain state. The hypothesis that homopolymers equivalent to the first block polymerized are the cause of anomalous micellization has been advanced previously,21,29 but apparently has not been definitively established nor generally accepted.1 To establish whether it is the correct explanation, the following experimental tests are clearly indicated: 1. The residual PS should be detectable (although admittedly only very small quantities may be present). 2. If the residual PS can be removed by fractionation, the anomalous micellization should vanish.

3. If a small amount of PI homopolymer equivalent to the second block polymerized were added to the sample, then anomalous micellization should be induced in the PS-selective solvents. 4. The high temperature onset of anomalous micellization should correspond approximately to the cloud point for a dilute solution of homopolymer in a solvent selective for the other copolymer component. In the following, we undertake all four of these tests and find that the results confirm the hypothesis. Figure 3 shows two SEC traces of SI(15-15) in THF, using a refractive index detector. One trace corresponds to the original sample as used in these studies, and the other to the sample after preparative chromatography has been used. The main peaks have been normalized to the same maximum, and the small horizontal offset is simply due to run-to-run fluctuations in instrument performance. The crucial feature is the small bump evident in the original sample centered at an elution volume of 24.2 mL, which has disappeared after purification. This is exactly where a PS homopolymer with M ) 15 000 would be expected to elute. On the basis of the relative heights of the peaks and the relative refractive index increments of the two blocks in THF, this homopolymer peak indicates that about 1% of the PS blocks did not cross over and initiate isoprene polymerization. We have examined other SI copolymers prepared in this laboratory30,32 and find that similar peaks are often observed, but that they are not always easily resolved from the baseline. Figure 4a shows the values of Rh for SI(15-15) in tetradecane, before and after purification, and Figure 4b shows the scattered intensity. The result is clear; after purification, there is no anomalous micellization. Furthermore, the resulting cmt corresponds closely to the lower temperature boundary of the anomalous region, supporting the hypothesis that this boundary of the anomalous region is due to resolubilization of the homopolymer after the normal micelles have formed. This particular solution was re-examined approximately 18 months later, with identical results; consequently the anomalous micelles do not reappear once the homopolymer has been removed. There is a third set of points in Figure 4a, obtained from fitting the intensity correlation functions to a sum of two exponentials. An example of such a fit is shown in Figure 5, for this solution at 105 °C. The slower mode corresponds to the anomalous structures, but the (32) Lodge, T. P.; Hanley, K. J.; Pudil, B.; Alahapperuma, V. Macromolecules 2003, 36, in press.

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Figure 4. Micellization of SI(15-15) in tetradecane before and after fractionation: (a) hydrodynamic radius versus temperature; (b) scattered intensity (normalized to the value at low temperature) at a scattering angle of 90° versus temperature.

faster mode can be attributed to single copolymer chains. Indeed, these data agree closely to those obtained after purification, indicating that even in the presence of anomalous micellization, some copolymer chains undergo normal micellization as T decreases. Figure 6 shows the scattered intensity for a solution of a PI homopolymer with M ) 11 000 (PI-11) in the PSselective solvent DEP, as a function of temperature upon slow cooling. Between 85 and 90 °C, the intensity begins to increase markedly, thereby providing an estimate of the cloud point where the PI solution undergoes liquidliquid phase separation. A small amount of this homopolymer was then added to SI(8-7) (ca. 1 wt % of copolymer), and a solution was prepared in DEP. The resulting values of Rh are shown as a function of temperature in Figure 7, along with the data for the original copolymer from Figure 1b. As hypothesized, the introduction of the PI homopolymer has induced anomalous micellization in the PS-selective solvent, and the onset of the effect corresponds well to the cloud point for the homopolymer. Note that this observation is in accordance with previous studies in which visible turbidity was observed; presumably the amount of homopolymer present will influence the “visibility” of the anomalous structures.

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Figure 5. Intensity correlation functions for solutions within the anomalous micelle regime: (a) SI(15-15) in tetradecane at 105 °C; (b) SI(8-7) in DEP at 60 °C, with 1% PI-11 homopolymer added.

Figure 6. Scattered intensity versus temperature for a 1% solution of PI-11 in DEP.

Discussion The results presented here support an appealingly simple explanation of anomalous micellization in diblock copolymers. A question of immediate importance, then, is whether this explanation is adequate to account for all the previous observations of anomalous micellization or whether additional phenomena are responsible. It turns

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Figure 7. Hydrodynamic radius versus temperature for SI(8-7) in DEP, with and without added PI-11 homopolymer. Table 1. Reports of Anomalous Micellization in Solutions of Diblock Copolymersa year (ref)

polymer

f

solvent

2nd block

selective for

1979 (5,6) 1983 (10) 1986 (13) 1987 (16) 1987 (15) 1993 (21) 2000 (26)

PS-PEP PS-P2VP P2VP-PtBA PS-PEO PS-PMMA PMA-PS PS-PDMS

0.38 0.23 0.80 0.13 0.57 0.23 0.20

decane/decalin toluene toluene water 1-chlorohexane water/dioxane DCB/BA

PEP P2VP PtBA PEO PMMA PMA PDMS

PEP PS PtBA PEO PS PMA PS

a Abbreviations: PS, polystyrene; PEP, poly(ethylene-alt-propylene); P2VP, poly(2-vinyl pyridine); PtBA, poly(tert-butyl acrylate); PEO, poly(ethylene oxide); PMMA, poly(methyl methacrylate); PMA, poly(methacrylic acid); PDMS, poly(dimethylsiloxane). The volume fraction of the first block is denoted by f.

out that, based on the published information, it is not possible to provide a definitive answer to this question, but as will emerge from the following discussion, most of the reported results could be taken to be consistent with our hypothesis. For reasons that will become apparent, the situation for triblocks is much more complicated than for diblocks, and so we will consider diblocks first. Table 1 presents a summary of reports of anomalous micellization in solutions of diblock copolymers, in chronological order.5,6,10,13,15,16,21,26 The important columns to focus on are those labeled “2nd block”, for the second block polymerized, and “selective for”, indicating which block is in good solvent conditions. To be consistent with the results presented here and the proposed “first block homopolymer” hypothesis, the entries in these two columns should match. In fact, in four cases they do match, and in three, they do not. At first glance, therefore, one might conclude that the first block homopolymer hypothesis does not provide a universal explanation for anomalous micellization. However, before adopting this stance, it is worth considering additional factors. There are actually at least two mechanisms by which homopolymer of the second block polymerized could be formed during the polymerization. One case involves species present in the initiator that are insufficiently active to polymerize the first monomer but are active enough to polymerize the second. The second case involves a chain transfer to solvent or monomer during the crossover to the second monomer, which then leads to homopolymerization of the second block monomer (as well as terminated homopolymer corresponding to the first block).

In the work of Fukumine et al.,26 the polymer in question was PS-PDMS (PDMS, poly(dimethylsiloxane)); the authors took care to extract any PS homopolymer. However, the reported polydispersity of the diblock was 1.23, which certainly indicates that some aspect of the polymerization was poorly controlled. The preparation of PDMS is well-known to have characteristics of an equilibrium polymerization, and thus higher polydispersity is expected if the reaction is allowed to run too far toward completion. The authors did not comment on whether the polymerization was deliberately terminated early, or not.26 Of course, substantial polydispersity of the second block would not produce PDMS homopolymer by itself, but it could possibly induce anomalous micellization through the composition heterogeneity mechanism. On the other hand, in our own laboratory we have found measurable amounts of PDMS homopolymer in the preparation of PIPDMS diblocks, which we have tentatively attributed to alkoxide impurities in the initiator that can only polymerize PDMS.33 We found these homopolymers to be broadly distributed in molecular weight, which made them rather difficult to detect by routine SEC, but they could be removed by fractionation. In short, we conclude that there is sufficient uncertainty about the composition of this sample that although the anomalous micellization cannot be attributed to first block homopolymer, it might well be due to contaminants of the second block. In the work of Duval and Picot, the polymer in question was PS-PMMA (PMMA, poly(methylmethacrylate)), dispersed in the PS-selective solvent in 1-chloro-n-hexane.15 No residual PS homopolymer was detected in the sample by SEC; the authors did not comment on the possible presence of PMMA. The results reported are similar to other reports of anomalous micellization in some respects, but not all. For example, the angular dissymmetry increased markedly, as did the radius of gyration (up to 1500 Å), within the anomalous regime. However, the associated molecular weight of the scattering objects, inferred from extrapolation to zero scattering angle, implies an association number on the order of 10. This combination of large radius and small aggregation number implies a highly extended association of just a few chains, which would be highly unusual. The situation with respect to ABA triblocks is even more complicated, as noted previously, for at least the following reasons. First, there are three different chemical routes to the triblock architecture, each with its own more probable contaminants. These are (i) sequential polymerization, (ii) coupling of diblocks, and (iii) difunctional initiation. Possible impurities due to incomplete crossover or initiation include the following: A homopolymer and AB diblock for (i), where the composition of the diblock would be much richer in B than the triblock; A homopolymer and AB diblock for (ii), where in this case the diblock would be “composition-matched” to the triblock; B homopolymer and BA diblocks for (iii), where the diblocks could be either B-rich or composition-matched. Second, in many reports the details of the synthesis were not provided, and/or the polymers were of commercial origin, and such information is not readily available. Third, there are differences in the tendency to micellization for an ABA triblock depending on whether the solvent is A-selective or B-selective; in the latter case the entropic penalty to placing both B blocks in a single core discourages (but by no means prevents!) closed-association micellization.1,22,34 (33) Wang, X.; Dormidontova, E. E.; Lodge, T. P. Macromolecules 2002, 35, 9687. (34) Balsara, N. P.; Tirrell, M.; Lodge, T. P. Macromolecules 1991, 24, 1975.

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Such differences could play a role in determining whether a contaminant species would be more or less likely to micellize a few degrees before the predominant triblock. Due to these factors, it is not really feasible for us to assess whether homopolymer or copolymer contaminants, or both, lead to anomalous micellization in triblocks; detailed characterization on the actual samples would be required. However, the work of Chu and co-workers with PEOPPO-PEO and PPO-PEO-PPO samples of commercial origin provides compelling evidence for the crucial role of contaminants, as they concluded.17,18,22 By careful filtration of the anomalous micelle solutions, they were able to remove the effect, and chemical analysis of the residue recovered from the filter confirmed a chemical composition rich in the less soluble component. In some relevant studies, the presence of wormlike micelles has been inferred, and in some cases even established by careful electron microscopy.7,14 Because the wormlike assemblies give rise to larger hydrodynamic radii and dissymmetry ratios, there has been a tendency to group these together with other reports of anomalous micellization. However, we feel that a useful distinction may be drawn, in that formation of wormlike micelles may be the thermodynamically preferred option for a pure copolymer sample, independent of any contaminants.1,35 Furthermore, in some instances the wormlike micelles do not intervene between dissolved chains and spherical micelles, as the anomalous micelles do, but actually result from cooling already formed spherical micelles.14 Indeed, this is consistent with general considerations of surfactant and copolymer self-assembly, namely, that as the unfavorable interaction between the solvent and the unfavored block increases spherical structures are formed first, and then cylindrical or wormlike assemblies. The spherical structures have more entropy but greater surface area, so that as the strength of the interactions increases the resulting curvature of the interfaces decreases. Summary The micellization behavior of two symmetric SI block copolymers in four solvents has been investigated by dynamic light scattering. Normal micellization is seen in the styrene-selective solvents DEP and DMP, whereas anomalous micellization is observed in the isopreneselective solvents tetradecane and squalane. A series of supporting experiments establish that anomalous micellization is due to the presence of small quantities of PS homopolymer, which presumably arise due to incomplete crossover to the second block during the sequential living (35) Won, Y. Y.; Davis, H. T.; Bates, F. S. Science 1999, 283, 960.

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anionic polymerization. As temperature is lowered toward the cmt, the homopolymer is driven toward liquid-liquid phase separation, but this process is arrested by the copolymer, leading to large structures that we propose are emulsion-like droplets. Upon further cooling, the cmt is reached, at which point the trace homopolymer is solubilized within the cores of compact micelles. Careful SEC analysis confirms the presence of the homopolymer contaminant, and after its removal by fractionation the anomalous micellization disappears. Similarly, anomalous micellization can be induced in the styrene-selective solvents by the addition of small amounts of PI homopolymer, and the onset of anomalous micellization occurs at the cloud point for the homopolymer. We discuss the possibility that this explanation for anomalous micellization is universal. In most reported cases for diblock copolymers, there is good reason to expect small amounts of homopolymer contamination, and thus this explanation is viable. Unfortunately, the requisite detailed characterization information is not available to test this hypothesis fully. Homopolymer contaminants of the second block are also possible, due to chain transfer events and/or initiator impurities. The majority of reported examples of anomalous micellization involve ABA triblock copolymers, where the possibilities for contamination due to incomplete crossover are increased. Furthermore, the different schemes of polymerization for triblocks, which are often left unspecified in the papers, would lead to different kinds of contaminants. Consequently, it is not possible to assess whether the hypothesis applies in these cases. However, our results do confirm that anomalous micellization is caused by an impurity, which can either be removed or added as desired. Furthermore, as our polymers are symmetric and very narrowly distributed, yet the effect is only seen in isoprene-selective solvents, we conclude that statistical fluctuations in composition are not sufficient to cause anomalous micellization in this system. Acknowledgment. This work was supported by the National Science Foundation though Award DMR9901087 and in part by the MRSEC Program under Award Number DMR-0212302. Furthermore, the MRSEC REU program provided support (S.D., J.O.), as did the Undergraduate Research Opportunities Program of the University of Minnesota (B.S.). We appreciate the assistance of T. Chang, Postech, and his group for the purification of one sample, and helpful discussions with M. Hillmyer and R. Quirk. LA0268808