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The effects of block copolymer molecular weight (MW) and composition on the critical micelle concentration (CMC) were studied using ionic liquids (ILs...
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Apparent Critical Micelle Concentrations in Block Copolymer/Ionic Liquid Solutions: Remarkably Weak Dependence on Solvophobic Block Molecular Weight Michelle M. Mok,† Raghuram Thiagarajan,‡ Maritza Flores,§ David C. Morse,‡ and Timothy P. Lodge*,†,‡ †

Department of Chemistry and ‡Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States § Department of Mechanical Engineering, University of Texas Pan American, Edinburg, Texas 78539, United States S Supporting Information *

ABSTRACT: The effects of block copolymer molecular weight (MW) and composition on the critical micelle concentration (CMC) were studied using ionic liquids (ILs) as model solvents. Pyrene fluorescence was used to measure CMCs as a function of block MW for three polystyrene−poly(ethylene oxide) (PS−PEO) samples and three PS−poly(methyl methacrylate) (PS−PMMA) samples in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide. The CMC decreased by a modest factor of 1.5 in the PS−PEO series, in which the solvophobic PS block MW remained unchanged (20 000) while the PEO block MW was decreased from 13 000 to 5000. This result correlated reasonably well with calculations from self-consistent-field (SCF) theory. A greater decrease (factor of 5) was seen in the PS−PMMA series, where the solvophobic PS block MW was varied from 3000 to 11 000 while maintaining a constant overall MW (ca. 15 000). However, this decrease was much weaker than that predicted by SCF calculations. A compilation of literature CMC data for amphiphilic block copolymers in water generally reveals a strong dependence on solvophobic block degree of polymerization N for low N, but a much weaker dependence for longer solvophobic blocks. From master plots of the compiled data, a scaling parameter shift from CMC ∼ exp(−cN) to CMC ∼ exp(−cN1/3) was found above a critical solvophobic block N. The parameter c correlates with the χ parameter between the solvophobic block and the solvent. The weaker N dependence was found to fit the IL data very well. While such a change in MW dependence has previously been attributed to the collapse of unimer solvophobic blocks, we also discuss the potential role of kinetic limitations.

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INTRODUCTION In conventional solvents, it is well-established that amphiphilic molecules at dilute concentrations will self-assemble into micelles. This process is driven by the minimization of contact between the solvent and the solvophobic regions of the amphiphile. Ionic liquids (ILs) are a relatively new class of solvents composed exclusively of ions.1 Specific advantages that they offer over traditional solvents include negligible volatility, tailorable solubilization, and high thermal and chemical stability. In ILs, micellization of small-molecule surfactants has been widely shown,2 but only rather recently were ILs also demonstrated to function as self-assembly media for block copolymers.3 A series of polybutadiene−poly(ethylene oxide) (PB−PEO) diblock copolymers in an IL formed the expected range of micellar structures (i.e., spherical, wormlike, and vesicular) found for block copolymers in “traditional” solvent systems. Since this initial report, micelle formation has been demonstrated for a range of copolymer systems in a variety of different ILs.4−12 The use of ILs rather than traditional solvents offers unique advantages for studying basic properties associated with micellization since, with their low melting points and negligible © 2012 American Chemical Society

volatility, they can be used in the liquid phase over a very large temperature range. This is especially useful for studies centered on the kinetics and thermodynamics of block copolymer micelles, which can present significant energetic barriers and long time scales for equilibration compared to small-molecule surfactants.13−19 The option to anneal IL-based solutions at high temperatures for extended time periods expands previous experimental boundaries. Researchers have found both upper and lower critical micellization temperatures (UCMTs and LCMTs) when scanning over temperatures up to 230 °C,7−9,11 using polymer blocks which present either upper or lower critical solution temperatures (UCSTs or LCSTs, respectively) in ILs.11,20−25 Homopolymers demonstrating LCSTs yielded block copolymers with LCMTs,7,11 while doubly thermoresponsive diblock copolymers exhibited both an LCMT and a UCMT.8,9 Other studies have explored the process of block copolymer micelle equilibration by monitoring their structures as a function of heating at extended times.26,27 Even after Received: February 25, 2012 Revised: May 9, 2012 Published: May 21, 2012 4818

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prolonged annealing at temperatures as high as 200 °C, the resulting structures remained path dependent due to barriers against unimer exchange. Finally, a recent study took advantage of the nonvolatility of ionic liquids for use as a solvent medium in measuring the glass transition temperature of block copolymer micelle cores.28 Here, we use ILs as model solvents to study the dependence of the critical micelle concentrations (CMCs) on block copolymer molecular weight. With the negligible volatility of ILs, it is straightforward to prepare block copolymer micelle solutions of any concentration through the selective and complete removal of a volatile cosolvent by exposure to vacuum. This sidesteps any complications associated with removing secondary solvents used to aid dissolution of copolymers. It also avoids kinetically trapped “frozen micelles” below the CMC that can potentially result from preparing lower concentration samples by direct dilution from higher concentrations.29,30 We confirm the applicability of pyrene fluorescence for CMC determination in block copolymer/IL systems for a variety of ILs and apply the pyrene fluorescence method in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([EMI][TFSA]) to determine CMCs in two different diblock copolymer systemspolystyrene−PEO (PS−PEO) and PS−poly(methyl methacrylate) (PS−PMMA)with varying block molecular weights. In the PS−PEO series, a constant molecular weight for the solvophobic block (PS) is maintained while varying the solvophilic block molecular weight (PEO); in the PS−PMMA series, composition is varied while maintaining an overall constant molecular weight. Finally, these results are compared with predictions from self-consistent-field theory and to prior results in aqueous and organic solvents. CMC and Solvophobic Block Molecular Weights. Theoretical treatments of the CMC for both small-molecule and polymeric surfactants generally predict that the CMC decreases approximately exponentially with the length of the solvophobic block (N), i.e., CMC ∼ exp(−cN). Here c is a constant that is related to the free energy cost per monomer for transferring the solvophobic block from the micelle core to solvent.31 This transfer free energy is found to be both larger and more strongly N-dependent than other contributions to the total free energy of a micelle and thus to dominate the Ndependence of the CMC. In self-consistent-field calculations for block copolymer micelles, the constant c depends upon the Flory−Huggins interaction parameter (χ) between the solvophobic block and the solvent, and approaches c = χ − 1 in the limit χ ≫ 1 of a nonsolvent.32−35 Such calculations also predict that the CMC depends much less strongly on the length of the solvophilic corona block than on the solvophobic core block.33,36 Experimental work on small-molecule surfactants shows that the CMC varies as CMC ∼ exp(−cN) with the number of solvophobic repeat units (N) for sufficiently small N.37−40 In studies of surfactants with longer solvophobic blocks, however, the dependence of the apparent CMC upon N becomes significantly weaker. In studies of conventional surfactants in water, where the hydrophobic block is an alkyl chain, a constant decrease is seen for ln(CMC) with each additional alkyl chain carbon up to N = 16 and much weaker dependence of ln(CMC) on N for larger N.37,38,40 Experimentally determined CMCs for amphiphilic diblock copolymers in many copolymer/solvent systems exhibit analogous behavior, with a stronger dependence on the length

of the solvophobic block for shorter, more soluble blocks than for longer, less soluble blocks, as shown for example in data compiled in refs 41−43. This is exemplified in Figure 1, where

Figure 1. Critical micelle concentrations as a function of solvophobic block length (N) in monomer repeat units for sodium alkyl sulfonate surfactants,45 PS−poly(sodium acrylate) (PS−PANa),46 PS/PEO copolymers,44 poly(butylene oxide)/PEO (PBO/PEO) copolymers,47−59 PPO/PEO copolymers,60,61 poly(styrene oxide)−PEO (PSO−PEO),62−64 poly(DL-lactide)−PEO (PL−PEO),65−71 poly(εcaprolactone)−PEO (PCL−PEO),72−75 and poly(valerolactone)− PEO76 in water.

(molar) CMC data are plotted as a function of N (in monomer repeat units) for a variety of micelle systems in water.44−76 The strongest dependences are observed in systems with low N and high CMCs, consistent with observations from small-molecule surfactant systems, while the weaker dependences are generally observed in systems with N > ∼20 and correspondingly lower CMCs. Some of the systems shown exhibit a crossover from strong dependence at lower solvophobic block lengths to a weaker dependence at higher block lengths within a homologous series of copolymers (PL−PEO, PS−PANa, PCL−PEO, PBO−PEO−PBO, PVL−PEO). Eisenberg and co-workers42,77 have shown that, for a variety of diblocks in which the CMC exhibits a weak dependence on N, the observed dependence can be fit to a function CMC ∼ exp(−aN1/3 + b). This functional form was found to fit data for diblock copolymers in both aqueous and organic solvents42,77 and even heteroarm star copolymers in organic solvent.78 In order to determine the degree of quantitative consistency among studies of different systems, while allowing for differences in solubility for different monomer−solvent pairs, we have attempted to collapse the data shown in Figure 1 by plotting ln(CMC) vs cN, rather than ln(CMC) vs N, where c is a constant that assumes different values for different monomer−solvent pairs. Figure 2a shows a master plot that we have created by choosing a value of the constant c for each monomer−solvent pair so as to as visually superimpose data for different systems. The quality of the collapse would be unchanged if we multiplied all of the resulting values of c by a common factor. We have thus arbitrarily taken c = 1 for systems of PBO−PEO−PBO and PEO−PBO−PEO in water. The data collapse cleanly to reveal two distinct regions of behavior: strong cN dependence for systems with CMC > 10−4 M or cN < ∼ 20, and much weaker cN dependence for systems with lower CMCs. The values used for c in each system are 4819

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Figure 2. (a) Master plot of CMC as a function of cN for aqueous micelle solutions created by rescaling data from Figure 1 by a multiplying factor (c). Values of c are provided in the legend in parentheses. (b) Comparison of master plot data to lines representing CMC ∼ exp(−Nx), for x = 1 (solid line), 2/3 (dashed line), and 1/3 (dotted line). Arbitrary vertical shifts (2, −1.3, and −4.4 for x = 1, 2/3, and 1/3, respectively) were applied to the logarithmic curves to best match the CMC data.

given in Table 1. Also listed are χcore−water values taken from the literature (where available)42,79−82 as well as the core-forming

solvent interactions. Collapse of the solvophobic block of the dissolved free molecules reduces the free energy cost of solvating free surfactant and thus shifts the equilibrium between the free molecules and micelles toward free molecules. In SCF calculations, the core block of a dissolved free molecule is treated as a random walk in almost pure solvent, for which the free energy cost of contact with the solvent is linear in the chain length. It is known, however, that a sufficiently long homopolymer in poor solvent will collapse into a globule with an interior concentration that (in the limit of very long chains) approaches that of the solvent-rich phase of the macroscopic polymer−solvent two-phase system. For a diblock copolymer system, the concentration in the interior of the globule formed by a single molecule with increasing N is also expected to become increasingly similar to that in the interior of a micelle of many chains. In the limit of very long chains, the largest contribution to the free energy ΔG to transfer the core block from a micelle into solvent thus eventually arises from the interfacial tension of the globule formed by free surfactant molecules. Because the radius for a single-molecule globule is proportional to N1/3, its interfacial area and interfacial free energy will be proportional to N2/3. When this interfacial contribution dominates ΔG, one expects a CMC that decreases as CMC ∼ exp(−cN2/3) with increasing N. This was the conclusion reached in a mean-field study by Marko and Rabin86 of micellization of charged diblocks with a neutral solvophobic block and a charged solvophilic block, where they assumed that the unimolecular state consisted of the solvophobic block in a collapsed form and the charged, solvopholic block in an extended form. In both the strong- and weak-charge limits, the CMC dependence was predicted to scale as CMC ∼ exp(−cN2/3), for the reasons explained above. This dependence is weaker than that predicted by SCF theories but stronger than the empirical relation CMC ∼ exp(−cN1/3) proposed by Gao and Eisenberg.77 Gao and Eisenberg also proposed a theoretical model for the N-dependence of the CMC that predicts CMC ∼ exp(−aN1/3), in agreement with their observations. Their model is based on an unusual proposal for the structure of micelles near the CMC. They suggest that the core of the micelle near the CMC is an aggregate of globules formed by collapsed solvophobic blocks

Table 1. Multiplying Factors (c) for Figure 2a, χcore−water, and δcore for Aqueous Micelle Systems

a

system (core/corona)

c

PPO/PEO sodium alkyl sulfonates PBO/PEO PL/PEO PVL/PEO PS/PANa PCL/PEO PSO/PEO PS/PEO

0.3−0.5 0.8 1−1.5 1.2 2 3 4 4 5

χcore−water [ref]a 0.7 [79] 2 [80] 3.4 [81] 3−4.4 [42, 82]

3−4.4 [42, 82]

δcore (MPa1/2)b 16.0 17.1 16.8 21.2 20.7 18.7 20.1 18.3 18.7

b

Literature values. Calculated using group contribution methods from tables of Small.83,84

block solubility parameters (δcore) calculated using group contribution methods from the tables of Small.83,84 Reasonable correlation is found between the ranking of c values required to superimpose the CMC data and those of χcore−water and δcore; this demonstrates that c is largely reflecting solvophobicity differences between the core-forming blocks. Many authors have suggested that the change in the Ndependence of the CMC with increasing N in both smallmolecule and diblock copolymer systems could be caused by a collapse of the solvophobic block of dissolved free molecules into a globule when this block is sufficiently insoluble.36,42,43,63,64,77,85 Such a model of unimer collapse was used by Booth et al. to explain data exhibiting changes in CMC dependence on N.43,63,64,85 These results were compiled from experimental studies of different block copolymers in water with PEO as the solvophilic block, where they had observed breaks in the N-dependence for certain systems. As already noted, the CMC is approximately proportional to the Boltzmann weight exp(−ΔG/kT) associated with the free energy cost ΔG to transfer the solvophobic block of a surfactant from the core of a micelle to a solvent environment, due to the differences in monomer−monomer and monomer− 4820

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Table 2. Molecular Characteristics of PS−PEO and PS−PMMA Diblock Copolymers sample

Mn,PS (kDa)a

Mn,total (kDa)b

Mw/Mna

f PSc

NSO or NSMc,d

CMC (wt %/vol %c)

SO(20−13) SO(20−8) SO(20−5) SM(3−13) SM(7−8) SM(11−4)

20 20 20 3 7 11

33 28 25 16 15 16

1.06 1.08 1.04 1.01 1.02 1.01

0.64 0.74 0.82 0.21 0.50 0.76

116 100 90 54 52 54

0.13/0.18 0.12/0.17 0.088/0.12 0.40/0.53 0.14/0.19 0.078/0.11

a Determined using size exclusion chromatography. bCalculated from Mn,PS and compositions from 1H NMR spectroscopy. cCalculated on the basis of mole fractions from 1H NMR and bulk densities of PS (1.05 g/cm3), PEO (1.20 g/cm3), and PMMA (1.18 g/cm3). dCalculated relative to the volume of [EMI][TFSA] (257.6/cm3 mol−1).

results that follow, we consider this possibility by using SCF theory to estimate the free energy barrier relevant to the spontaneous formation of micelles, as functions of concentration and chain length, in addition to calculating equilibrium CMCs.

of individual polymers (“unimer micelles”), with a separate interface around each such globule, and they estimate the binding free energy of the micelle by modeling van der Waals attractions between such unimer globules. We know of no experimental evidence for this model structure of a micelle core and are therefore skeptical of this analysis. On the basis of simple interfacial area arguments, we anticipate that the scaling CMC ∼ exp(−cN2/3) is correct in the limit of extremely long chains and thus expect the progressive collapse of the unimer solvophobic block to yield a smooth crossover from CMC ∼ exp(−cN) to CMC ∼ exp(−cN2/3) with increasing N. In Figure 2b, we compare the collapsed data to different functional forms CMC ∼ exp(−cNx) with x = 1, 2/3, and 1/3. As noted in the figure caption, a multiplicative (vertical) shift was applied to the curves in an attempt to fit the data. A value of x = 1 gave an excellent fit to the data at lower cN, suggestive of a freely dissolved, uncollapsed unimer conformation when the solvophobic block is of low molecular weight. A value of x = 1/3 gives a good fit to the data at high cN, as found previously by Eisenberg and co-workers.42,77 This is a weaker dependence than that proposed by the interfacial area argument (x = 2/3). A modification to this basic model that could potentially explain the weakened dependence is that the collapsed solvophobic blocks are partially shielded from interactions with the solvent through the rearrangement of the solvophilic block.87 It is also possible that the observed change in behavior with increasing N is a kinetic effect rather than an equilibrium effect. The suggestion by previous workers that the weak Ndependence of the CMC could be a result of the collapse of the solvophobic block is an equilibrium argument, which assumes that the CMC measured in experiment is the equilibrium CMC. Meanwhile, the spontaneous creation and destruction of micelles near the CMC are thermally activated processes with rates that are normally controlled by free energy barriers.13,14 These barriers tend to grow with increasing length of the solvophobic block and are expected to become prohibitive for sufficiently insoluble surfactants. Like nucleation barriers, the barrier to micelle creation depends on concentration: a solution that cannot form micelles at experimentally observable time scales at the equilibrium CMC may form micelles readily if the concentration of unimers is raised (“supersaturated”) above some kinetic threshold somewhat greater than the CMC. Experiments that attempt to measure the CMC in systems in which spontaneous micelle creation and destruction is not rapid at the equilibrium CMC could measure an apparent CMC that is actually controlled by kinetic effects. The observed weak dependence of the apparent CMC could be explained if the experiments measured a kinetic threshold concentration that has a weaker dependence on N than the equilibrium CMC. In analyzing the block copolymer/IL CMC

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EXPERIMENTAL SECTION

Materials and Solutions. The PS−PMMA (SM) and PS−PEO (SO) diblock copolymers were previously synthesized by Smith88 and Simone,89 respectively, using sequential living anionic polymerization. They were characterized using size exclusion chromatography and 1H NMR spectroscopy; the molecular characteristics of the copolymers are given in Table 2. The samples were designated as SO(X−Y) or SM(X−Y), where X and Y refer to the average block molecular weights in kDa. The SO series samples all have constant PS-block molecular weight (20 kDa), while the SM series samples are of almost constant total molecular weight (∼15−16 kDa). Polystyrene (Mn = 2 kDa, PDI = 1.06) was purchased from Pressure Chemical Co. The ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([EMI][TFSA]) was prepared as described previously90,91 from [EMI][Br] (IoLiTec) and [Li][TFSA] (3M). The ionic liquids 1-butyl-3-methylimidazolium/TFSA ([BMI][TFSA]) and 1-hexyl-3-methylimidazolium/TFSA ([HMI][TFSA]) were prepared using analogous methods, from the same [Li][TFSA] and [BMI][Cl] or [HMI][Cl]. The [BMI][Cl] was synthesized from 1-methylimidazole and 1-chlorobutane as described previously.23 The [HMI][Cl] was synthesized from as-purchased 1-methylimidazole (Sigma-Aldrich, 96 g) and 1-chlorohexane (Sigma-Aldrich, 141 g), based on a procedure described by Nockemann et al.92 The reaction was initially carried out in toluene (325 mL) at 47 °C for 72 h, and then the temperature was increased to 70 °C under reflux for 24 h. The product was washed with toluene three times and dried in a vacuum oven at room temperature (RT) for 48 h. The IL EMI/ tetrafluoroborate ([EMI][BF4]) was prepared as described in ref 23. All final IL products were clear and colorless. Stock solutions with 2 wt % copolymer were prepared by combining the copolymer and IL at appropriate weight ratios and adding excess methylene chloride as a cosolvent to facilitate dissolution. These solutions were stirred until homogeneous. The cosolvent was then removed by a gentle nitrogen purge at RT for >24 h, followed by placing in a vacuum oven (∼60 mTorr) at RT for 4 h. We note that all these 2 wt % copolymer in [EMI][TFSA] solutions have previously been demonstrated to contain micelles with hydrodynamic radii ∼10− 100 nm, based on dynamic light scattering; please refer to ref 28 for full Rh and size distribution data. The remaining concentrations for each series were prepared by a stepwise dilution from the 2 wt % stock solution by adding the appropriate volume of IL at each step. Each of these dilutions was then redissolved in methylene chloride and dried using the procedure described for the 2 wt % solution. For the [EMI][TFSA] solutions measured using pyrene fluorescence, the pyrene was incorporated directly into the IL (2.5 × 10−6 g pyrene/g IL) prior to preparation of the stock solution and subsequent dilutions. It was found that 4 h of drying under vacuum was sufficient to yield consistent fluorescence results (unchanged from 1 h of drying under vacuum), but not so long that there was any 4821

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Figure 3. Normalized (a) excitation spectra (λem = 389 nm) and (b) emission spectra (λex = 339 nm) of pyrene doped into pure PS and pure [EMI][TFSA]. significant evaporation of the pyrene probe. For the [BMI][TFSA], [HMI][TFSA], and [EMI][BF4] solutions, pyrene was incorporated after the solutions were dried in vacuum. This was done by preparing a stock solution of pyrene in acetone, adding the appropriate volume of solution to a vial and evaporating the acetone. The prepared copolymer/IL solutions were then added to the vials at the appropriate volume. Results from both methods of pyrene incorporation were found to be equivalent. All solutions were heated at 105 °C for 1 h with stirring prior to measurement to allow the micelles to equilibrate above the Tg of PS and to allow the pyrene to equilibrate within the solutions. After heating, the solutions were immediately cooled to room temperature and measurements were taken the same day. To prepare the sample of pyrene in pure PS, a vial containing pyrene (7.6 × 10−7 g) was prepared using a known volume of pyrene/ acetone stock solution from which the acetone was evaporated. To create a PS/pyrene mixture, ∼100 mg of PS was added to the vial, heated to 150 °C, and stirred for several minutes before cooling to room temperature. The sample was then broken into small pieces, transferred to a cuvette (1.5 mm path length), and heated to 190 °C to consolidate the sample. While some pyrene was likely lost upon heating, the normalized intensities should be unaffected. Fluorescence Measurements. Fluorescence measurements were taken using a Photon Technology International QuantaMaster 40 steady-state spectrofluorometer at room temperature (20−21 °C) in a right-angle geometry. The solutions prepared from SO(20−13), SO(20−8), SM(3−13), and SM(7−8) were measured in a cuvette with a path length of 10 mm. The solutions prepared from SO(20−5) and SM(11−4) were measured in a cuvette with a shorter path length (1.5 mm) to reduce noise from scattering. Measurements were taken using 1 nm slits under excitation and 1 nm slits under emission for the 10 mm path length cell and 1.3 nm slits under excitation and 1.5 nm slits under emission for the 1.5 mm path length cell. Details of temperature-based fluorescence measurements can be found in the Supporting Information. Dynamic Light Scattering (DLS). Details of temperature-based DLS measurements can be found in the Supporting Information. Self-Consistent-Field (SCF) Calculations. Calculations were carried out for the copolymers using a real space formulation for a micelle with spherical symmetry based on the procedure described by Chang and Morse.35

advantage of the sensitivity of the pyrene emission spectrum to the polarity of its local environment.93,94 Specifically, the emission spectrum consists of five well-defined peaks between ∼365 and 400 nm, where the intensity of the first peak is significantly enhanced relative to the other peaks in more polar solvents. Typically, the intensity ratio of the first and third spectral peaks (I3/I1) is used as a relative measure of polarity, with higher values reflecting less polar environments. By choosing a surfactant system where pyrene molecules will preferentially segregate to the micelle cores, the I3/I1 value will reflect that of the solvent at concentrations below CMC but will shift to that of the micelle core once micelles form.93 This technique has been applied for CMC determination in aqueous systems for both small-molecule surfactants93,95,96 and block copolymers.97−100 One previous report101 used pyrene for CMC determination of small-molecule surfactants within an IL. Specifically, Fletcher and Pandey were able to detect a shift in I3/I1 for four surfactants in [EMI][TFSA] above a certain concentration, indicating aggregation. Additionally, a number of studies have employed the I3/I1 ratio to study properties of other systems containing ILs, including neat ILs,102,103 IL/water mixtures,103 IL/homopolymer mixtures,104 the effect of adding ILs to water/ surfactant systems,105,106 the conformation of pyrene endlabeled homopolymers in IL,107 and determining the polarity of supported IL phases.108 All of these works employed imidazolium cation-based ILs,101−108 indicating that pyrene fluorescence should be a viable method in these IL systems. As a note, one report has determined that measurements of I3/I1 could not be applied to study IL self-aggregation in water for the case of pyridinium cation-based ILs, as the pyridinium group led to quenching of pyrene fluorescence.109 To demonstrate the applicability of pyrene fluorescence for determining CMCs in PS-based block copolymer systems, we first examine its spectra in PS and [EMI][TFSA] (the refractive indices of PS and [EMI][TFSA] are 1.59 and 1.43, respectively). Figures 3a and 3b show the normalized excitation and emission spectra, respectively, for pyrene doped into pure PS and pure [EMI][TFSA]. Both excitation spectra in Figure 3a exhibit three peaks, with the PS spectrum shifted to longer wavelengths compared to the [EMI][TFSA] spectrum (e.g., the third peak shifts from 333 to 338 nm). A similar shift has previously been observed in water/PS systems (333−339

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RESULTS AND DISCUSSION Pyrene Fluorescence for CMC Determination. In this section we explore the potential for using the fluorescence properties of free pyrene dye to determine CMCs for PScontaining block copolymers in ILs. This technique takes 4822

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nm).44,97 Also, we note a decrease in the normalized intensities of the first and second excitation peaks of the PS sample compared to the [EMI][TFSA] sample. The emission spectrum of the PS sample in Figure 3b is also shifted to slightly longer wavelengths relative to that of the IL sample. More importantly, the relative intensity of the third peak is significantly reduced in [EMI][TFSA] (I3/I1 = 0.47) compared to that in PS (I3/I1 = 0.93). These values are consistent with previously reported values for this IL28,101 and for PS.44,98 Next, we examine pyrene excitation spectra after SO(20−8) is added to [EMI][TFSA]. Figure 4 shows the normalized

highest concentration samples are not as far above the CMC as the highest concentration water/PS−PEO samples. Second, pyrene may not partition as strongly between [EMI][TFSA] and PS as it does between water and PS,97 and so we see greater contributions from pyrene in the solvent phase. Finally, there may be some finite amount of IL in the PS micelle cores. Regardless of the level of partitioning, it is still possible to target pyrene molecules which have segregated to less polar environments through the choice of excitation wavelength, as in the water/PS−PEO systems.44,97 Figures 5a and 5b show the normalized emission spectra of the SO(20−8) concentration series excited at 333 and 339 nm, respectively. Using λex = 333 nm targets the pyrene population in [EMI][TFSA], and the samples show only a minute increase in I3 at the highest concentration. Meanwhile, using λex = 339 nm emphasizes pyrene molecules in a less polar environment, and the samples show a much more substantial increase in I3, beginning at intermediate concentrations. Plotting these I3/I1 values as a function of concentration (Figure 6), we obtain curves analogous to those obtained from CMC studies based in aqueous systems. Finally, in the Supporting Information we demonstrate the applicability of this technique for determining CMCs in other imidazolium-based ionic liquids[BMI][TFSA], [HMI][TFSA], and [EMI][BF4]. Results reflected trends seen for solubility by these different cations and anions in studies of CMCs, CMTs, and homopolymer solubilization (see Supporting Information for more detailed discussion). Researchers studying water/PS−PEO systems had also used integrated emission intensities as a function of concentration to determine CMCs.44,97 We did not find this to be applicable in our systems (see Supporting Information Figure S3), as the overall emission intensities were mostly governed by minor variations in absorption intensity, yielding changes which were insubstantial and noisy compared to those in the aqueous studies. Effect of Block Copolymer Composition on CMCs. Having established that the pyrene method can be employed for CMC determination in block copolymer/IL solvent systems, we now discuss the results of its application to the PS−PEO and PS−PMMA block copolymer series (Figure 6). As mentioned earlier, in the series of PS−PEO block copolymers, composition is varied by maintaining a constant molecular weight for the solvophobic block (PS) while varying

Figure 4. Normalized excitation spectra (λem = 389 nm) of pyrene in the SO(20−8) block copolymer concentration series in [EMI][TFSA].

spectra for this system as a function of copolymer concentration from pure [EMI][TFSA] to 2 wt % copolymer. Overall, the changes in the spectra indicate some level of partitioning of pyrene to a more PS-like environment, with a slight shift to longer wavelengths and a reduction in the relative intensities of the first and second peaks. These shifts in wavelength are not as drastic as those seen in water/PS−PEO systems,44,97 where at the highest concentrations studied, the third peak had entirely shifted to 339 nm. This is likely due to some combination of the following factors. First, even the

Figure 5. Normalized emission spectra taken at (a) λex = 333 nm and (b) λex = 339 nm of pyrene in the SO(20−8) block copolymer concentration series in [EMI][TFSA]. 4823

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Figure 6. I3/I1 ratios as a function of concentration for (a) PS−PEO and (b) PS−PMMA block copolymers (λex = 339 nm) in [EMI][TFSA]. Dashed lines are exponential fits to the data.

larger shift for the PS−PMMA series is generally consistent with the increase in PS-block molecular weight (4 to 13 kDa). In a following section, a direct comparison of these results to theoretical predictions is presented. Studies as a Function of Temperature. We also performed a preliminary temperature-based investigation of the micellization and demicellization of the block copolymer/ [EMI][TFSA] systems. We were interested in seeing whether a shift from micelles to unimers could be detected with increasing temperature. Studies were carried out using DLS and fluorescence on the two block copolymers with the lowest PS-block molecular weights, SM(3−13) and SM(7−8), since these should present the lowest solvophobic drive to remain in micelles. Apparent Rh distributions from DLS (as given by the Laplace inversion routine REPES) for SM(7−8) at 0.5 wt % (c/ CMC = 3.6) as a function of temperature are shown in Figure S4. A single, narrow peak between 10 and 20 nm, corresponding to micelles, is observed at all temperatures. A very slight shift to higher Rh is observed with increasing temperature, but there is no discernible shift in population from micelles to free chains up to 200 °C. (Measurements were not taken to higher temperatures due to the potential for polymer degradation.) The SM(3−13) case exhibited a similar lack of population shift as a function of temperature (data not shown). Measurements taken by fluorescence as a function of temperature support these findings by DLS of micelles stable against noticeable shifts in phase behavior at higher temperatures (see Supporting Information). Discussion with Relation to Aqueous Systems. Here, we examine whether the relatively high CMCs observed for our block copolymer/IL systems are consistent with previous observations in more conventional solvent systems. The one reported CMC value for PS−PEO (1−3 kDa) in an IL ([BMI][BF4]) was ∼0.5 wt %,110 comparable to our CMC values in magnitude. Relative to our SO(20−13) in [BMI][TFSA] results (CMC = 0.13 wt %), both the overall molecular weight and PS molecular weight of this block copolymer are much lower and should yield an increased CMC, but the BF4− anion is more hydrophilic/basic than TFSA− and should yield a decreased CMC (see Supporting Information); it appears these effects largely cancel each other out. Relative to studies of PS−PEO block copolymer micelle formation in water, the CMCs reported in ILs are substantially

the solvophilic block molecular weight (PEO); in the PS− PMMA series, composition is varied while maintaining an overall constant molecular weight. In every sample, we see evidence of micelle formation, as I3/ I1 begins to increase above the baseline [EMI][TFSA] value once a certain concentration is exceeded. The general point at which this increase emerged shifts much more between different samples in the PS−PMMA series than in the PS− PEO series. Also, the cases with the highest PS fraction in each series (SO(20−5) and SM(11−4)) exhibited I3/I1 increases at the lowest concentrations, consistent with PS being the solvophobic block driving micelle formation. There have been various approaches in the literature to identify CMC values from I3/I1 plots as a function of concentration.44,96,98 Given that we have not captured the end to the shift in pyrene partitioning, we cannot apply a sigmoidal fit to our results. Moreover, given the curvature present in the data, it is not simple to fit our results with two straight lines. Instead, we apply a method where the data are fit to exponential curves, and the CMCs are defined at the point where the curves exceed a threshold value (I3/I1,threshold). We defined I3/I1,threshold as a value 2% greater than the baseline I3/I1 value; this was chosen as being sufficiently close to the transition but outside the range of noise (±0.005) for the room temperature measurements. This method captures the relative locations of CMCs for different samples self-consistently; however, by definition, it does slightly overestimate the actual CMC values. This overestimation is within the variation between different previous means of defining CMCs.96 The CMC values calculated using this method are compiled in Table 2. In the PS−PEO series, the CMC increases by a factor of 1.5 from SO(20−5) to SO(20−13); this increase is virtually negligible relative to the noise levels of the system. Meanwhile, in the PS−PMMA series, the CMC increases by a factor of 5.1 from SM(11−4) to SM(3−13). Theory predicts that block copolymer CMCs shift with molecular weight,32 with a much greater impact from changes to the solvophobic block molecular weight than the solvophilic block molecular weight.33−36 Thus, the relatively smaller shift for the PS− PEO series is consistent with theory, since the solvophobic PS block remains at a constant molecular weight (20 kDa) through the series while it is the solvophilic PEO-block molecular weight that changes from 5 to 13 kDa. Meanwhile, the relatively 4824

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higher, e.g., reported values for water are on the order of 1−5 × 10−4 wt %;44,97 this is 2 or more orders of magnitude lower than what we observed in our PS−PEO/IL measurements. These results are consistent with previous measurements of small-molecule surfactant CMCs in [BMI][BF4], where the CMCs in the IL were 2−4 orders of magnitude higher than those in water.111,112 This was attributed to the much weaker solvophobic effect of the ILs compared to the equivalent hydrophobic effect of water.112,113 These effects arise from the entropy loss associated with the oriented arrangement of the solvent molecules around the surfactant hydrocarbon tails for structured solvation;114 this loss was found to be higher in water than in the IL. Supporting this notion of a reduced solvophobic effect in ILs, it was noted that PS−PEO block copolymers with greater than 50 mol % PS macroscopically phase separated in water (concentrations not specified),44 whereas two out of the three PS−PEO block copolymers in this study (SO(20−8) at 51 mol % PS and SO(20−5) at 63 mol % PS) had more than 50 mol % PS and still formed stable micelles in [EMI][TFSA]. Related to these results, the micellization of a Pluronic triblock copolymer (F68) has been studied in both water115 and ILs.6 In water, its CMC was measured as 10 wt % or greater at 30 °C, while in [BMI][PF6] at 25 °C its CMC was much higher (∼30 wt %). Finally, one report on small-molecule surfactant micellization in mixtures of water and [BMI][BF4] as solvent found a greater than 1 decade increase in CMC value from that of water alone for a solvent mixture containing 30 wt % [BMI][BF4].106 Overall, while the CMC values for our block copolymer/IL systems are relatively high compared to block copolymer/traditional solvent systems, they are in line with trends observed for other surfactants studied in ILs compared to water. Comparison to Theory. Self-consistent-field (SCF) calculations of equilibrium CMCs were carried out for these solutions and compared to experimental results. Independently estimated values were used for all parameters except for the interaction parameter χPS‑IL, which we treated as adjustable because the CMC is extremely sensitive to the value chosen for this parameter. The adequacy of the theory can then be assessed by examining how well the data for different chain lengths and corona blocks can be described using a single value for χPS‑IL. Styrene volume fractions (f PS) and the copolymer degrees of polymerization (NSO and NSM) are given in Table 2. These degrees of polymerization are defined as ratios of the polymer molar volumes to the solvent volume, 257.6 cm3 mol−1, using densities of 1.05 g/mL for styrene, 1.20 g/mL for PEO, and 1.18 g/mL for PMMA. All interaction parameters used in the SCF calculations are scaled to the solvent reference volume. No precise values are available for the corona−solvent interaction parameters, but [EMI][TSFA] has been shown to be a good solvent for both PEO and PMMA.23,91,116 Results of SCF calculations are not very sensitive to the value chosen for this parameter over the range of values 0.34−0.5 typical of good solvents, so a value of χ = 0.4 was used for the corona−solvent interaction parameters χPEO‑IL and χPMMA‑IL.82,117 The PEO−PS interaction parameter was calculated based on its reported temperature dependence determined from order−disorder transition data to yield χPEO‑PS = 0.36.118,119 The PMMA−PS interaction parameter was calculated based on its reported temperature dependence by neutron scattering to yield χPMMA‑PS = 0.11.120

Figure 7 shows the results of SCF predictions for SO(20−8) over a range of possible values of χPS‑IL between 0.8 and 1.2.

Figure 7. Critical micelle concentrations calculated as a function of χ PS‑IL from SCF for SO(20−8). Dashed lines indicate the experimentally determined CMC (0.17 vol %) and the corresponding value of χPS‑IL (0.84).

The predicted CMC is extremely sensitive to the value of this parameter. Adjusting χPS‑IL so as to fit the observed CMC of 0.17 vol %, as measured by fluorescence, yields an estimated value of χPS‑IL = 0.84. This relatively modest value is consistent with observations of terminal relaxation behavior in a triblock copolymer network of PS−PEO−PS ( f PS = 0.16) with 3 kg/ mol PS end blocks in [EMI][TFSA], indicating that the thermodynamic penalty is low enough for the PS end blocks to be pulled out of the micelle cross-links and dragged through the PEO/[EMI][TFSA] matrix.29 With χPS‑IL = 0.84 and NPS = 11 for this system, the value for χPS‑ILNPS is 9.2. This value of χPS‑IL = 0.84 was then used to predict CMC values for the two remaining SO polymers. The predicted CMC is primarily controlled by the length of the core block and the magnitude of the core−solvent interaction, with only a weak dependence on the length of the corona block.32−36 As the three SO polymers all had PS core blocks of the same length, SCF predicts rather similar CMCs for these three polymers, 0.23 vol % for SO(20−13) and 0.12 vol % for SO(20−5), in rough agreement with the experimental values (0.18 and 0.12 vol %, respectively). This comparison was thus successful but confirms only that the apparent CMC is relatively insensitive to the length of the corona block. Attempts to use SCF to rationalize the experimental results were less successful for the SM polymers, which have substantially different solvophobic block lengths. Theory predicts a CMC that varies with core chain length as approximately exp(−f(χ)N)),32−35 where N is the length of the core block and f(χ) is a function of χ that approaches f(χ) = χ in the nonsolvent limit χ ≫ 1, but that has a somewhat weaker dependence on χ for the more modest values of χPS‑IL ∼ 1 explored here. The SM core block with the longest styrene block SM(11−4) has a PS core block that is almost a factor of 2 lower than the PS core block of any of the SO series, but a CMC that is similar to that of SO(20−5). Using the same value of χPS‑IL for both series, with any reasonable choice of values for the other interaction parameters, would yield a much higher predicted CMC for SM(11−4) than for SO(20−5). Choosing 4825

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χPS‑IL so as to fit the observed CMC of SM(11−4) yields a value of χPS‑IL = 0.94 that is only slightly higher than that obtained for SO(20−5) because the CMC is so sensitive to the value of the parameter. There is no value for this parameter, however, that can fit the observed weak dependence of the CMC on core block length within the SM series. Using χPS‑IL = 0.94, so as to fit the observed CMC of SM(11−14), yields predicted CMC value of 0.64 vol % for SM(7−8), compared to an observed value of 0.19 vol %. More importantly, with this choice of χ parameters, SCF theory predicts that SM(3−13) should be completely soluble and should not form micelles at all. It is, of course, possible to pick a value of χPS‑IL so as to fit the CMCs of either SM(7−8) or SM(3−13) alone, which yield 1.1 and 1.7, respectively, but SCF theory always predicts a much stronger CMC dependence on PS core block length than that which is observed. As such, we evaluate whether the CMC vs N dependence of our systems can be described using the same weaker dependence found for aqueous and organic micelle systems which was discussed in an earlier section. A direct comparison of our IL data to a curve representing CMC ∼ exp(−N1/3) yielded quantitatively comparable results (Figure 8). (Note that

nuclei larger than the critical size grow only to the equilibrium micelle size (as a result of chain stretching energy) rather than growing without bound. The free energy barrier to micelle creation is found to depend on the concentration of dissolved single molecules, as well as molecular weight and other parameters, and to decrease with increasing copolymer concentration. It is thus possible, for some choices of parameters, for the barrier to be prohibitive (≫10 kT) at the equilibrium CMC, but to drop to a value that allows micelle creation at observable rates when the concentration of copolymer unimers exceeds some higher threshold value for association, which we refer to as the association concentration. If so, the apparent CMC identified in experiments like those presented here would be the kinetic association concentration rather than the equilibrium CMC. We previously found that, for AB copolymers in an A homopolymer matrix, this association concentration can be several orders of magnitude above the equilibrium CMC. For the systems studied here, using the modest values of the parameter χPS‑IL required to reproduce the observed CMC (interpreted as either an equilibrium CMC or a kinetic threshold), we find that the barriers are relatively small. In Figure 9, the dotted line (where it does not overlap the solid

Figure 8. Comparison of curve representing CMC ∼ exp(−N1/3) (solid line) to PS−PMMA and PS−PEO CMC data in [EMI][TFSA] as a function of hydrophobic block length (N). A vertical shift of −2.1 was applied to the logarithmic curve.

Figure 9. Critical micelle concentrations calculated as a function of χPS‑IL from SCF for SM(7−8). The dashed line indicates the apparent CMC or kinetic association concentration while the solid line shows the equilibrium CMC.

the CMCs are plotted in units of mol/L for ease of comparison against the aqueous data.) This strongly suggests that block copolymer micellization in ILs follows a similar path to that of the other solvent systems, with a reduced N-dependence based on either equilibrium effects or kinetic effects. We used SCF theory to assess the hypothesis that the weak dependence of the observed CMC on solvophobic chain lengths could be the result of a kinetic limitation. The process by which the samples were prepared, cosolvent evaporation, requires that micelles be created as the cosolvent is removed. The spontaneous formation and dissolution of micelles are activated processes that can be slow even for small molecule surfactants and that are controlled by free energy barriers that are known to grow rapidly with increasing molecular weight. Two of us recently showed how SCF theory could be used to estimate the free energy barrier that is relevant to these processes and thus estimate rates of creation and destruction.14 The underlying theory for micelle creation is closely analogous to the classical theory of nucleation, except for the fact that

line) represents the concentration required to reduce the free energy barrier to 10 kT, as an estimate of the kinetic association concentration. At low values of χ, where the dotted and solid line overlap, the barrier is already less than 10 kT at the equilibrium CMC, which would allow rapid spontaneous micelle creation at the equilibrium CMC, implying that for this range of parameters the apparent CMC should correspond to the equilibrium CMC. A more detailed study of the dependence of the barrier upon both χ and N (not shown) shows that, in the range of parameters relevant to these experiments, the association threshold concentration is sometimes higher than the CMC, but only slightly higher, and its dependence on solvophobic block length is thus only slightly weaker than that predicted for the CMC and much stronger than observed in these experiments. We therefore conclude that this way of estimating effects of kinetic limitations also cannot 4826

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Science Foundation under Award DMR-0934157, and through the Minnesota Supercomputing Institute. We acknowledge Dr. Hau-Nan Lee for supply of the [EMI][BF4] and [BMI][TFSA] and assistance with [HMI][TFSA] synthesis and Prof. Andrew Taton and Jun Sung Kang for providing access and training on the spectrofluorometer.

explain the observed weak dependence on solvophobic block length. We have not quantitatively examined the possible effect of collapse of the core block of dissolved single molecule unimers upon the equilibrium between unimers and micelles, as suggested by other authors. This phenomenon is expected to occur for sufficiently insoluble core blocks but is not easily treated in SCF theory, which treats individual chains as random walks. It is not at all clear, however, whether the modest values of interaction parameter suggested by the comparatively high CMC values found for the systems studied here are large enough to cause the core block of these polymers to collapse into globules or to have a significant effect upon the CMC. Finally, in addition to impacting the equilibrium between micelles and unimers, there is also the potential that there is a direct impact from the collapse of the core block on micellization kinetics. These are important questions that deserve more careful scrutiny than we can provide here.

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CONCLUSIONS A pyrene fluorescence technique was applied in ILs to study the dependence of the CMC on block copolymer molecular weight. The decrease in CMC was small in a PS−PEO series, where the solvophobic PS block molecular weight remained unchanged while the PEO block molecular weight was increased. Reasonable correlation was found against predictions from self-consistent-field theory for this series. A greater decrease in CMC was seen in a PS−PMMA series, when the solvophobic PS block molecular weight was varied while maintaining a constant overall molecular weight. However, this decrease was still much weaker than that predicted by SCF calculations. A compilation of CMC data in water from the literature generally revealed a strong dependence on solvophobic block MW at lower MW, but a weaker dependence at higher MW. From master plots of the compiled data, a scaling parameter shift from CMC ∼ exp(−cN) to CMC ∼ exp(−cN1/3) was found above a critical solvophobic block MW, suggesting either a change in unimer conformation or kinetic limitations. The weaker dependence was found to fit our IL data very well. It remains an important challenge to explain the weak dependence of the CMC on solvophobic block length within the context of a molecular theory.

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ASSOCIATED CONTENT

S Supporting Information *

Discussion and figures related to fluorescence results in different ionic liquids; figure related to unnormalized pyrene fluorescence spectra as a function of concentration; methods, figures, and further discussion related to studies as a function of temperature. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the NSF through Award DMR0804197 (T.P.L.), by the MRSEC Program of the NSF under Award DMR-0819885, the PREM program of the National 4827

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