Critical micelle concentrations of block and gradient copolymers in homopolymer: Effects of sequence distribution, composition, and molecular weight



The critical micelle concentrations (CMCs) of styrene–methyl methacrylate (S-MMA) block and gradient copolymers present in a homopolymer poly(methyl methacrylate) (PMMA) matrix were determined using an intrinsic fluorescence technique based on the ratio of excimer to monomer fluorescence from styrene repeat units. The homopolymer molecular weight (MW) and copolymer MW, composition, and sequence distribution were varied to determine their effects on the CMC, and comparisons were made to theory. Although the effects of these parameters on micelle formation have been the focus of significant theoretical study, few experimental studies have addressed these issues. The MW of the S block (forming the micelle core) has a strong effect on the CMC. For example, an order of magnitude reduction in the CMC (from ∼ 1 to ∼ 0.1 wt %) is observed when the S block MW is increased from 51 to 147 kg/mol while maintaining the MMA block and PMMA MWs at 48–55 kg/mol. Increasing the PMMA matrix MW also has a strong an effect on the CMC, with the CMC for a nearly symmetric S-MMA block copolymer with each block MW equal to 48–51 kg/mol decreasing by a factor of 5 and by several orders of magnitude when the matrix MW is increased from 55 to 106 kg/mol and 255 kg/mol, respectively. In contrast, similar changes in the MMA block MW have little effect on the CMC. Finally, when present in a 55 kg/mol PMMA matrix, a 55 kg/mol S-MMA gradient copolymer with a styrene mole fraction of 0.51 exhibits a factor of 6 larger CMC than a block copolymer of similar MW and composition. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2672–2682, 2008


The addition of low levels (∼ 5 wt % or less) of block copolymer to homopolymer or immiscible homopolymer blends can result in materials of significant technological and fundamental scientific interest. For example, addition of appropriately selected block copolymer during mixing of immiscible polymer blends has been the subject of study over several decades as a strategy for blend compatibilization,1–9 that is, controlling the dispersed-phase domain size and preventing coarsening of such dispersed-phase domains during subsequent high-temperature melt processing. In such applications, block copolymer is added as an interfacial agent, with each block species being miscible in one of the homopolymers. Successful compatibilization relies on block copolymer being located at the interface between the immiscible blend components, where it reduces interfacial tension, which aids in droplet breakup during melt processing, and provides steric hindrance to coalescence.2, 10–12 However, the efficacy of block copolymers as blend compatibilizers can be severely reduced because of their thermodynamically driven tendency to form micelles when present at concentrations above a critical micelle concentration (CMC) in homopolymer; block copolymer trapped in micelles does not affect the interfacial activity of the blend.2

Fundamental theoretical interest in the factors that impact micelle formation by block copolymer present in homopolymer also dates back several decades.13–18 This theoretical work has largely focused on factors that impact the micelle formation of block copolymer dispersed within a homopolymer matrix, specifically the molecular weight (MW) of components in the blend and the thermodynamic incompatibility of the comonomers. The first theoretical study of A–B diblock copolymers dispersed in homopolymer A, by Leibler et al.,13 predicted a strong effect of monomer incompatibility on the CMC. That is, with all other factors being equal, an increase in the value of the Flory-Huggins interaction parameter (χ) results in a reduced CMC. Whitmore and Noolandi14 predicted similar behavior in a model system of styrene–butadiene diblock copolymer dispersed in polybutadiene homopolymer. Additionally, they determined that the CMC depends strongly on the MW of the block that makes up the core of the micelle; for example, when the MW of the styrene block in the copolymer is increased by a factor of two, the CMC decreases by two orders of magnitude. In contrast, they found that an increase in the MW of the shell block results in only a minor increase in the CMC. Both the theory by Leibler et al.13 and the modification by Roe15 predict a strong dependence of the CMC on homopolymer MW, with an increase in homopolymer MW leading to a decrease of the CMC.

Despite the long-standing theoretical interest and technological significance of the CMC for block copolymer in homopolymer, there are few experimental reports of well-characterized CMC values of block copolymer within homopolymer.19–24 Rigby and Roe19, 20 used small-angle x-ray scattering to determine the CMC of styrene–butadiene block copolymer in polybutadiene. After making corrections to obtain interpretable x-ray data, they extrapolated plots of scattering intensity as a function of copolymer concentration to zero intensity, yielding a measurement of the CMC. Kinning et al.21, 23 used transmission electron microscopy to determine CMC values in blends of low levels of styrene–butadiene diblock copolymer in polystyrene (PS). Each CMC value was obtained by sampling at least 20 images and calculating the number of micelles per unit area as a function of copolymer concentration. Determining the CMC by transmission electron microscopy can be error prone if there is inhomogeneity in the distribution of micelles in the homopolymer or if the micelles or the CMC is extremely small.

Fluorescence nonradiative energy transfer (NRET, also called fluorescence resonance energy transfer or FRET) has also been employed to determine micelle formation in mixtures of styrene–isoprene diblock copolymers in polyisoprene.22 In a 1990 FRET study from our group, Major et al.22 reported a strong sensitivity of the CMC to homopolymer MW. For example, for styrene–isoprene diblock copolymer with each block MW being ∼ 3 kg/mol, no CMC was evident up to 10 wt % block copolymer in mixtures with polyisoprene of MW between 2 and 9 kg/mol. However, when the polyisoprene matrix MW was 11 kg/mol or greater, micelles were evident at 1 wt % or lower copolymer concentration. We also observed a strong effect of block copolymer MW on micelle formation, with a 10–11 kg/mol styrene–isoprene diblock copolymer exhibiting micelle formation at ∼ 0.1 wt % concentration in blends with polyisoprene having MWs of 2 and 9 kg/mol.22 We also reported an increase in the amount of free block copolymer in the homopolymer with increasing concentration above the apparent CMC,22 an observation that was also made in the studies by Kinning et al.21

Besides its utility in studying micelle formation in homopolymer, fluorescence can provide outstanding sensitivity to extremely low CMCs, for example, 0.001–0.0001 wt %, in mixtures of block copolymer with low MW solvent.25–28 However, in most cases, these studies require either the use of specially synthesized, fluorescent-dye-labeled block copolymers for NRET or FRET measurements or the incorporation of external fluorescence probes that provide sensitivity to local polarity and segregate to micelle cores. Thus, such approaches rely on extrinsic fluorescence for their sensitivity to micelle formation.

Recently, our group developed a novel and very simple fluorescence technique to determine the CMC values of styrene-containing block copolymer in a nonfluorescent homopolymer matrix, with the demonstration being made using a styrene–methyl methacrylate (S-MMA) block copolymer dispersed within a poly(methyl methacrylate) (PMMA) matrix.24 This technique takes advantage of the intrinsic fluorescence of the styrene repeat units in the copolymer. In solutions of PS or styrene-containing block copolymer or random copolymer (with significant styrene content) in low MW solvent, the intrinsic fluorescence spectrum exhibits two peaks, one centered at ∼ 280–285 nm and the second at ∼ 330 nm.29–34 The lower wavelength peak, called monomer fluorescence, is due to emission from single, excited-state phenyl rings; the higher wavelength peak is due to emission from excited-state dimers formed when a single excited-state phenyl ring comes into a sandwich-like arrangement with a second phenyl ring with a 0.3–0.4 nm separation distance.35 The latter emission is called excimer fluorescence and in dilute solution results nearly exclusively from excimer formation involving S–S dyads (nearest neighbor styrene units) along the chain backbone.29 A sensitivity of the PS emission spectrum to high local concentration of styrene units has been observed during phase separation in immiscible blends and microphase separated block copolymers36–38 and has even been used to quantify the kinetics of phase separation.36, 37 It is this sensitivity that we exploited in our proof-of-principle study24 demonstrating the applicability of the excimer to monomer fluorescence intensity ratio in the determination of the CMC of S-MMA diblock copolymer in PMMA.

In the same study,24 we also showed that this approach can be used to determine the CMC of S-MMA gradient copolymer in PMMA. Gradient copolymers possess a gradual change of comonomer composition along the length of the copolymer chain.39–59 (For a review and comparison of gradient copolymer structure relative to that of other copolymers, see ref. 49.) Using self-consistent field theory, Shull41 predicted that gradient copolymers exhibit a substantially lower CMC than do block copolymers of similar MW and composition. This was confirmed in our recent publication.24 Because of their unique composition profiles, gradient copolymers have also been shown to exhibit an unusually broad glass transition temperature43–45 (Tg) and to be effective in compatibilizing immiscible polymer blends.46–48, 59 The higher CMC values associated with gradient copolymers means that, on addition to an immiscible blend, gradient copolymers are less likely than block copolymers to be trapped in micelles and thus are able to affect the interfacial activity of the blend more easily than block copolymers.

Here, we apply our simple intrinsic fluorescence technique to a broad study related to the characterization of the CMC in mixtures of copolymer with homopolymer. We have chosen to work with the S-MMA copolymers in PMMA based on several factors. First, the S-MMA system is relatively weakly segregating (the Flory-Huggins interaction parameter is 0.037–0.038 at temperatures above Tg60), which should ensure the CMC values can be determined by obtaining data over easily accessible ranges of copolymer concentration in homopolymer. Second, there is commercial availability of well characterized, nearly monodisperse S-MMA block copolymer of many compositions and MWs, providing a facile way to study the effects of block copolymer MW and composition on the CMC. Additionally, our current study also investigates how the CMC is affected by homopolymer MW and copolymer sequence distribution, the latter via a comparison of results obtained with block copolymer and gradient copolymer of similar overall composition and MW.


S-MMA diblock copolymers were purchased from Polymer Source and used as received. Table 1 lists the block copolymer characteristics provided by the supplier. To employ concise designations of the copolymers in the remainder of the paper, we have devised a simple method of abbreviation. For example, we use the abbreviation 51S-b-48MMA in the case of a S-MMA diblock copolymer with reported number average MW (Mn) of the S and MMA blocks of 50.6 and 47.6 kg/mol, respectively. PMMA samples were either made by conventional free radical polymerization (Mn = 55.2 kg/mol, PDI = 1.60, as determined by gel permeation chromatography using a universal calibration method relative to PS standards in tetrahydrofuran) or purchased as samples from Polymer Source (Mn = 106 kg/mol, PDI = 1.04; Mn = 255 kg/mol, PDI = 1.16) and used as received.

Table 1. Block Copolymer Characterizationa
Block Copolymer IdentificationStyrene Block Mn (g/mol)Methyl Methacrylate Block Mn (g/mol)PDI
  • a

    Determined by the supplier.


A S-MMA gradient copolymer was synthesized using nitroxide-mediated controlled radical polymerization. A unimolecular alkoxyamine initiator, 2,2,5-trimethyl-3-(1-phenylethoxy)-4-phenyl-3-azahexane (A29),53 was combined with S (7 mL; [A29] = 3.4 × 10−3 mol/L) in a test tube. (The synthesis of A29 followed the description in ref. 61.) The test tube was then placed in a 93 °C oil bath after N2 purging for 30 min. Addition of MMA to the test tube was performed from the beginning of the reaction, using a constant rate (2 mL/h) throughout the polymerization. The reaction was performed under N2 atmosphere, and aliquots of the reaction mixture were removed at 2 and 4 h of reaction time. The reaction was stopped after 8 h of reaction time. 1H-NMR was used to determine the styrene content of the copolymer (cumulative styrene mole fraction Fs = 0.51). Gel permeation chromatography (tetrahydrofuran as solvent) relative to PS standards was used to determine the apparent MW (Mn = 55,200 g/mol, PDI = 1.44).

Films of S-MMA copolymer and PMMA were prepared by solvent casting 8–9 wt % solutions of copolymer and PMMA in toluene (Aldrich) onto quartz slides. Films were allowed to dry in a solvent-rich environment at room temperature for 12 h, followed by 12 h at room temperature and laboratory atmosphere. Next, films were placed in a vacuum oven heated at 60 °C, with the temperature gradually increased to 150 °C over 2 days. Before measurement, films were annealed at 170 °C for 5 h to allow copolymers to reach equilibrium dispersion. Films were then removed from the 170 °C oven to room temperature conditions (far below the glass transition temperatures of the S and MMA blocks and PMMA), freezing the morphology of the blends.

Steady-state fluorescence measurements were taken at room temperature using a Photon Technology International fluorimeter. The excitation wavelength was 260 nm and emission spectra were taken over the wavelength range 270–370 nm; emission and excitation slits had band-passes of 2 and 4 nm, respectively. For further details on measuring intrinsic fluorescence from styrene-containing polymer films, see refs. 34 and 38.


Characterization of the CMC of S-MMA Block Copolymer in PMMA via Fluorescence

Figure 1 shows representative room-temperature fluorescence spectra at low and high concentration of 25S-b-26MMA block copolymer in a PMMA matrix with Mn = 55 kg/mol. At low copolymer concentration (0.001 wt %), there is one main peak centered at ∼ 280 nm, which is associated with monomer fluorescence, that is, emission from the singlet excited state of a phenyl ring that forms a side group of a styrene block repeat unit. In contrast, at high (8 wt %) block copolymer concentration in PMMA, two peaks are clearly evident, the more intense one from monomer fluorescence and the less intense one, centered at ∼ 330 nm, from excimer fluorescence.

Figure 1.

Fluorescence spectra of 25S-b-26MMA copolymer dispersed in 55 kg/mol PMMA (PDI = 1.6) at ( equation image) 0.001 wt % and (−) 8 wt % copolymer.

Consistent with our previous study,24 excimer fluorescence is virtually absent when S-containing block copolymer is present at trace levels in PMMA. The absence of excimer fluorescence has previously been reported in neat or solution-state random copolymer with very low S mole fractions,34 which can be explained by the absence of nearest neighbor S units along the copolymer chain backbone. The lack of excimer fluorescence in blends of PMMA with trace levels of S-containing block copolymers must result from two factors. First, when the trace copolymer is molecularly dispersed in the glassy PMMA, there is insufficient conformational mobility to achieve sandwich-like conformations of nearest neighbor phenyl rings during the several nanosecond lifetime of an excited-state phenyl ring. Second, at most a negligible population of conformations leading to direct excitation of excimer is present when S-containing copolymer is present at trace concentration in PMMA. The presence of some excimer fluorescence at higher copolymer concentration is evidence of micelle formation in the PMMA matrix,24 because micelles result in high local concentrations of styrene units in the micelle cores that accommodate excimer fluorescence via interpolymer excimer formation and energy migration effects.

In the remainder of the paper, we employ the ratio of fluorescence intensity at 330 nm to the fluorescence intensity at 280 nm (I330/I280) as a relative quantitative measure of the ratio of excimer fluorescence to monomer fluorescence. (By using an intrinsic excimer to monomer intensity ratio rather than an intensity as our measurable, our technique is self-referencing, that is, independent of the thicknesses of the various films used in our study. Other self-referencing measurables that are useful in film studies include fluorescence lifetimes,62, 63 wavelength-shifting dye fluorescence,64–66 and the ratio of excimer to monomer fluorescence from extrinsic dyes.67) When the ratio is close to zero and approximately independent of copolymer concentration in the blend, the copolymer concentration is below the CMC. At higher copolymer loadings where the ratio increases with increasing concentration, the copolymer is present at levels exceeding the CMC. We define the CMC value as the concentration at which I330/I280 begins to increase with increasing copolymer content.

Effects of the Composition of S-MMA Block Copolymer and the MWs of Block Copolymer and PMMA on the CMC

Using a plot of I330/I280 as a function of logarithmic block copolymer concentration, Figure 2 examines the effect on the CMC of the overall block copolymer MW at constant copolymer composition and constant PMMA MW. In particular, we maintain the styrene repeat unit content in the copolymer at ∼ 50 mol % and the PMMA matrix Mn value at 55 kg/mol. At sufficiently low concentration of each of the three block copolymers employed in this comparison, I330/I280 is ∼ 0.1 and approximately independent of copolymer concentration, consistent with each copolymer system being molecularly dispersed in the PMMA matrix. At sufficiently high concentration, I330/I280 increases with increasing concentration over the range of concentration investigated, consistent with the growing presence of block copolymer micelles with styrene-block cores.

Figure 2.

Effect on the CMC of overall S-MMA block copolymer MW with constant styrene composition: (□) 25S-b-26MMA, (○) 51S-b-48MMA, (▵) 170S-b-168MMA. Samples dispersed in 55 kg/mol PMMA (PDI = 1.6).

From Figure 2, it is evident that the CMC for the highest MW block copolymer, 170S-b-168MMA is ∼ 0.1 wt %. In contrast, the two lower MW block copolymers, 25S-b-26MMA and 51S-b-48MMA, have CMC values of ∼ 1 wt %. This order-of-magnitude difference in the CMC values can be ascribed to the MW ratio of the MMA block to the PMMA homopolymer. These effects are in accordance with those reported by Major et al.22 for systems consisting of styrene–isoprene block copolymer in polyisoprene. That is, there is little or no change in the CMC as a function of block copolymer MW when the shell block MW is equal to or one-half that of the homopolymer MW. However, when the shell block MW is significantly larger than the homopolymer MW, there is a major decrease in the CMC with increasing block MW.

Figure 3 reinforces the important effect on the CMC of the ratio of the MW of the matrix polymer to the MW of the block making up the shell of the micelle. In particular, Figure 3 compares the concentration dependence of I330/I280 for a 51S-b-48MMA block copolymer in blends with PMMA having Mn = 55 kg/mol or Mn = 106 kg/mol. At sufficiently low copolymer concentration, I330/I280 is ∼ 0.1 and independent of concentration; at high copolymer concentration, I330/I280 increases significantly with increasing concentration. In the 106 kg/mol PMMA matrix, the 51S-b-48MMA copolymer exhibits a CMC of ∼ 0.2 wt %,24 roughly a factor of 5 below that observed in the 50 kg/mol PMMA matrix. We also did experiments employing the same copolymer blended with 255 kg/mol PMMA. Over all block copolymer concentrations studied down to 0.001 wt %, 1.4 ≤ I330/I280 ≤ 1.9. (The data associated with the 255 kg/mol PMMA matrix are not shown in Figure 3 as the intensity ratio values are more than a factor of 2 greater than the maximum intensity ratio associated with the lower MW PMMA matrices.) This means that the CMC for this copolymer in the 255 kg/mol PMMA matrix is far below 0.001 wt % or more than three orders of magnitude smaller than the CMC obtained in the 55 kg/mol PMMA matrix. This very strong effect of matrix MW on the CMC when the ratio of matrix MW to shell block MW exceeds unity is in accord with theoretical expectations15 and deserves further study.

Figure 3.

Effect of PMMA matrix MW on the CMC of 51S-b-48MMA: (○) 55 kg/mol PMMA matrix (PDI = 1.6), ( equation image) 106 kg/mol PMMA matrix (PDI = 1.04) from Wong et al.24

Figure 4 examines the effect of copolymer composition on the CMC by employing two block copolymers (147S-b-54MMA and 47S-b-140MMA) of nearly identical overall MW in blends with 55 kg/mol PMMA. When the core block MW is roughly a factor of 3 larger than that of the shell block MW and the matrix MW, the CMC is ∼ 0.1 wt %. This is an order of magnitude smaller than the ∼ 1 wt % CMC that is observed when the core block MW is matched to that of the matrix but is only about one-third that of the shell block MW. The strong effect of the core block MW on the CMC is in accord with theoretical predictions.14

Figure 4.

Effect on the CMC of block copolymer composition at constant overall MW: (▿) 47S-b-140MMA, (⋄) 147S-b-54MMA. Samples dispersed in 55 kg/mol PMMA (PDI = 1.6).

Also worth noting is the fact that the highest values of I330/I280 reported in all of our figures are 1.3–1.4, which are observed at 4–10 wt % concentrations of the 147S-b-54MMA block copolymer (Fig. 4) and of the 170S-b-168MMA block copolymer (Fig. 2) in a PMMA matrix with Mn = 55 kg/mol. (In data not shown in the figures, I330/I280 = 1.9 at the highest concentration in films of 51S-b-48MMA block copolymer dispersed within the 255 kg/mol PMMA matrix.) These relatively high values of the ratio of excimer to monomer fluorescence intensity are associated with high local concentrations of the styrene units within the micelle cores and indicate that the micelle cores experience much less interpenetration by the MMA block or PMMA when the micelle cores are of high MW (or when the PMMA matrix MW greatly exceeds the MMA block MW). That is, the micelle cores are nearly pure styrene when the styrene block MW is approximately 150 kg/mol or greater, and the micelle cores have low but significant levels of MMA repeat units present when the styrene block MW is approximately 50 kg/mol or lower.

Figure 5 examines the effect of changing the MW of one block of the copolymer while maintaining nearly constant MWs of the second block and the PMMA matrix. Figure 5(a) compares I330/I280 values as a function of copolymer concentration for the 147S-b-54MMA and 51S-b-48MMA block copolymers. As described above, the CMC for the block copolymer with the 147 kg/mol styrene block is ∼ 0.1 wt % whereas the CMC for the block copolymer with the 51 kg/mol styrene block is ∼ 1 wt %. These results are consistent with theoretical expectation and previous experimental results that indicate that an increase in the core block MW results in a major reduction in miscibility with the matrix polymer.14, 15, 20 In contrast, Figure 5(b) indicates that there is no significant effect on the CMC when the shell MW is increased by a factor of 3 and is roughly equal to or greater than the matrix MW. These results are also in accord with theory.14

Figure 5.

(A) Effect of S block MW on the CMC: (⋄) 147S-b-54MMA, (○) 51S-b-48MMA. Samples dispersed in 55 kg/mol PMMA (PDI = 1.6). (B) Effect of MMA block MW on the CMC: (○) 51S-b-48MMA, (▿) 47S-b-140MMA. Samples dispersed in 55 kg/mol PMMA (PDI = 1.6).

Effect of the S-MMA Copolymer Sequence Distribution on the CMC in a PMMA Matrix Polymer: Comparison of Gradient Copolymer with Block Copolymer

Unlike S-MMA diblock copolymers, which are commercially available in a wide variety of compositions and MW, S-MMA gradient copolymers are available only via synthesis. Because of the pseudoliving nature of nitroxide-mediated controlled radical polymerization, the sequence distribution of the S-MMA gradient copolymer can be adjusted by controlling the comonomer concentration during reaction via the use of a semibatch polymerization.43 Figure 6 depicts the cumulative styrene mole fraction as a function of the apparent normalized MW of the gradient copolymer synthesized in this study. At the early stages of reaction when styrene is predominant in the comonomer mixture, the gradient copolymer is mostly styrene in composition. With increasing reaction time and as more MMA is added to the comonomer mix, there is both an increase in the apparent MW of the gradient copolymer being synthesized and a reduction in the cumulative mole fraction of styrene incorporated into the copolymer. Such an evolution of overall copolymer composition with apparent copolymer MW can be taken as proof of gradient copolymer formation. (See refs. 43, 45, and 49 for more detailed descriptions regarding the structures and properties of gradient copolymers.) On completion of the synthesis, the resulting gradient copolymer had a cumulative styrene mole fraction of 0.51 and an apparent Mn = 55.2 kg/mol.

Figure 6.

Cumulative styrene mole fraction of gradient copolymer as a function of apparent normalized MW. Inset: Schematic illustration of a gradient copolymer.

Analogous to the fluorescence spectra reported as a function of S-MMA block copolymer concentration in Figure 1, Figure 7 illustrates the fluorescence spectra for S-MMA gradient copolymer at low and high concentration in a PMMA matrix. At 0.001 wt % gradient copolymer, the fluorescence spectrum is very similar to that associated with the block copolymer in Figure 1. This result is consistent with the notion that S-MMA gradient copolymers exhibit monomer fluorescence nearly exclusively at room temperature when they are molecularly dispersed in PMMA. With 10 wt % gradient copolymer, there is an increase in the normalized fluorescence intensity in the neighborhood of 330 nm, an indication of the presence of excimer fluorescence, albeit less than that exhibited by the analogous block copolymer at 8 wt % concentration in Figure 1. The reduced capacity for gradient copolymers to exhibit excimer fluorescence relative to block copolymers is because of many fewer S–S dyads (neighboring repeat units) being present in a S-MMA gradient copolymer chain than in a block copolymer chain of similar composition

Figure 7.

Fluorescence spectra of S-MMA gradient copolymer with apparent Mn = 55 kg/mol and Fs = 0.51 dispersed in 55 kg/mol PMMA (PDI = 1.6) at ( equation image) 0.001 wt % and (−) 10 wt % copolymer.

Figure 8 examines the effect on the CMC of the overall sequencing of the comonomer units in the copolymer. In particular, we compare I330/I280 as a function of copolymer concentration for block and gradient copolymers with nearly identical overall MW and composition: 25S-b-26MMA block copolymer and gradient copolymer with Mn = 55.2 kg/mol and a cumulative styrene mole fraction of 0.51. In both cases, the PMMA matrix Mn is 55 kg/mol. At low concentration, both copolymers exhibit I330/I280 ∼ 0.1 that is independent of concentration, whereas at high concentration, I330/I280 increases with concentration. The gradient copolymer exhibits a CMC value of ∼ 6 wt %, or about a factor of 6 greater than that of the block copolymer. These results are in accord with our proof-of-principle study reported in 2007.24 In that study, we compared the CMCs obtained in S-MMA block and gradient copolymers that had Mn values of 110 and 102 kg/mol, respectively, and cumulative styrene mole fractions of 0.50 and 0.55, respectively. The copolymers were blended with nearly monodisperse PMMA having Mn = 106 kg/mol. With these systems, we observed CMC values of ∼ 0.2 and ∼ 2 wt % for the block copolymer and gradient copolymer, respectively. The higher CMC values observed in Figure 8 are expected based on lower overall MWs of the copolymers and matrix used in the current study relative to those used in the 2007 study.

Figure 8.

Effect of copolymer sequence distribution on the CMC: (□) 25S-b-26MMA, (◃) S-MMA gradient copolymer with apparent Mn = 55 kg/mol and Fs = 0.51. Samples dispersed in 55 kg/mol PMMA (PDI = 1.6).

The significantly higher CMC values for the gradient copolymers relative to the block copolymers of similar overall MW and composition are noteworthy at two levels. First, these results are qualitatively consistent with the theoretical predictions made in 2002 by Shull.41 Second, the significantly higher CMC values for the gradient copolymers are of potential technological importance in relation to compatibilization of immiscible blends. Because copolymers located in micelles do not contribute to blend compatibilization, low CMC values can disqualify the use as compatibilizers of particular block copolymers in combination with specific polymer blends. Although the CMC values observed in the current study of block copolymer mixtures with homopolymer are not alarmingly low, often near ∼ 0.1 wt %, it is likely that blend compatibilization via copolymer addition is not possible if the CMC is significantly less than 0.1 wt % (as in the case when the PMMA matrix MW is 255 kg/mol; see discussion above). However, the S-MMA copolymer/PMMA homopolymer system is relatively weakly segregating, and so it should be expected that the CMC values would be significantly higher in this system than in a typical immiscible blend of commercial interest. Consequently, it will be of great importance to extend the type of study described here to other more strongly segregating copolymer/homopolymer systems to determine whether the very low CMCs likely to be obtained in such systems containing block copolymer can be ameliorated by use of gradient copolymer. Investigations are underway.


We have demonstrated for a broad range of conditions the use of a simple intrinsic fluorescence technique to determine the CMC values of S-MMA block and gradient copolymers dispersed within PMMA homopolymer, which constitutes a weakly segregating system. This technique, which involves the measurement of an excimer to monomer fluorescence intensity ratio as a function of copolymer concentration, also provides sensitivity to the concentration of styrene repeat units within the micelle core. The MW of the styrene block that forms the core of the micelle has a strong effect on the CMC; for example, relative to a system in which the S block, MMA block, and PMMA MW are nearly identical, an increase by a factor of 3 of only the S block MW results in an order of magnitude reduction in the CMC. In contrast, a similar factor of 3 increase in the MW of the MMA block that forms the shell of the micelle has little effect on the CMC. This qualitative behavior is in accord with theory.14 Additionally, the MW of the homopolymer matrix has a strong effect on the CMC when the homopolymer MW exceeds that of the shell block. Finally, gradient copolymers exhibit significantly higher CMCs than block copolymers of similar overall MW and composition, also in agreement with theory.41 It will be important to extend this technique for characterizing CMC values in other styrene-containing copolymer/homopolymer systems that exhibit moderate-to-strong segregation strengths and to develop other simple, fluorescence-based techniques for characterizing micelle formation in copolymer/homopolymer systems that lack styrene-based repeat units.


We acknowledge the support of the NSF-MRSEC program (Grant DMR-0520513), a 3M fellowship (to J.K.), and Northwestern University. We also gratefully acknowledge Professor SonBinh Nguyen and Christine Dettmer from the Department of Chemistry at Northwestern University for the synthesis of the unimolecular initiator A29.