Addition of Corona Block Homopolymer Retards Chain Exchange in

Feb 11, 2016 - The exchange of copolymer chains between 1 vol % PS–PEP (poly(styrene-b-ethylene-alt-propylene)) diblock copolymer micelles in squala...
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Addition of Corona Block Homopolymer Retards Chain Exchange in Solutions of Block Copolymer Micelles J. Lu,† F. S. Bates,*,† and T. P. Lodge*,†,‡ †

Department of Chemical Engineering and Materials Science and ‡Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: The exchange of copolymer chains between 1 vol % PS−PEP (poly(styrene-b-ethylene-alt-propylene)) diblock copolymer micelles in squalane (selective for PEP) is investigated using time-resolved small-angle neutron scattering (TR-SANS) as a function of added PEP homopolymer. The solvent squalane, C30H62, is substituted in part or completely with PEP homopolymers that are the same molecular weight as the corona blocks. Polymer solutions/mixtures (1 vol % PS−PEP, plus 2, 7, or 15 vol % PEP in squalane, and 1 vol % PS−PEP in PEP) were separately prepared using normal (hPS) or deuterated equivalent (d-PS) PS−PEP diblock copolymers. The solvent was contrast matched to a 50/50 mixed h-/d-PS micelle core, so that the scattering intensity decays with the mixing of h- and d-PS−PEP chains undergoing exchange between micelles. The chain exchange rate can therefore be assessed quantitatively. As the concentration of added homopolymer in solution increases above the overlap concentration of PEP chains, the chain exchange rate drops significantly. The results are compared to an earlier study of chain exchange between PS−PEP micelles in a 15% solution in squalane, which was also found to be significantly slower than when the solution is dilute. The primary factor in this slowing down of chain exchange is an increased screening of excluded volume interactions among the corona blocks. The role of increasing micelle aggregation number with PEP concentration is found not to be the dominant effect up to 15% added PEP but may play an increasingly important role in the PEP melt matrix, where no chain exchange could be detected in these experiments.

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INTRODUCTION Block copolymer micelles1,2 exhibit much slower single chain exchange kinetics than aggregates of small molecule surfactants, and as a result nonergodicity is often observed.3−5 Understanding the kinetic processes for block copolymer micelles both at and far from equilibrium is crucial in controlling the formation of path-dependent micelle structures. Studies of block copolymer micelle exchange mechanisms are relatively recent compared to those on the kinetics of small molecule surfactants.6,7 In addition to fluorescence techniques,8−12 time-resolved small-angle neutron scattering (TR-SANS) has emerged as an invaluable tool to quantitatively characterize the micelle equilibrium process13−25 in a way that experimental complications are minimized. A theoretical analysis by Halperin and Alexander26 describes the role of core and corona blocks in chain exchange, for both “hairy” and “crew cut” micelles. While the dependence on core length has been widely studied,14,15,18,21−24 the corona block is often assumed to be less significant. However, Choi et al. found the chain exchange rate of 15 vol % poly(styrene)-blockpoly(ethylene-alt-propylene) (PS−PEP) micelles in squalane to be about 1 order of magnitude slower than that of 1 vol % PS− PEP micelles, implying a role for the corona blocks in the chain exchange process.22 The detailed explanation for the slower © XXXX American Chemical Society

kinetics in concentrated PS−PEP solutions is not yet clear. In a recent study of triblock copolymer chain exchange, an accelerating role of corona blocks was also clearly indicated.25 The rate of chain exchange in PS−PEP was compared with that for PEP−PS−PEP triblocks containing the same PS block size but with one additional PEP corona block; the latter system was found to be faster by about 3 orders of magnitude. One hypothesis is that the corona blocks can accelerate the chain extraction by experiencing a relief of chain stretching upon escaping into the solution; this concept is generally consistent with the earlier theoretical prediction by Halperin and Alexander.26 This result gives a clue to the role of corona blocks in chain exchange between micelles in concentrated solution. Namely, above the overlap concentration, the corona chains would be in a semidilute solution no matter whether inside the micelles or not, and therefore the chain extraction step is less favored. On the other hand, the screening effect of overlapped corona chains27 leads to an increased micelle size (aggregation number). This could make both the chain extraction and Received: November 3, 2015 Revised: January 30, 2016

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Time-Resolved Small-Angle Neutron Scattering. The d- and hPS−PEP micelles were separately prepared using a cosolvent method: polymers were dissolved in a mixture of selective solvent (squalane) and nonselective solvent of much lower boiling point (dichloromethane), followed by the removal of the latter. All micelle solutions were then annealed at 180 °C for 30 min to acquire an equilibrated structure.29 After the solutions were cooled to room temperature, PEP was added into the micelle solutions at 2, 7, or 15 vol % (designated as 2PEP, 7PEP, and 15PEP samples, correspondingly) and stirred until dissolved. Assuming the density of each block is the same as the corresponding bulk homopolymer, the relative amounts of d-/h−PS−PEP diblock polymers and PEP homopolymers were calculated to make the final concentration of PS−PEP micelles 1 vol %. The solutions were then stored at room temperature and used without further thermal annealing. The glass transition temperature of the PS cores in squalane is estimated to be about 70 °C, well above room temperature.33 Therefore, the size of PS−PEP micelles in solution mixtures remains the same as for 1 vol % micelles in pure squalane21 and does not depend on the concentration of added PEP. The d- and h-micelles in squalane/PEP mixtures were then blended (postmixed, thus forming unmixed micelle cores) at room temperature and loaded into sample cells for TR-SANS experiments. 1 vol % d- and h-PS−PEP micelles in pure PEP (99PEP) rather than squalane were also prepared by codissolving the polymers in dichloromethane, with the latter being slowly removed and the micelles being thermally annealed subsequently, as described above. However, as indicated by the TR-SANS results discussed below, no observable chain exchange between the 99PEP micelles occurs for up to 180 min at 200 °C. The d- and h-99PEP specimens were postmixed by redissolving them in the PEP-selective solvent pentane and then dried under vacuum. The possibility of significant chain exchange during this process is estimated to be small, as discussed in the Supporting Information.

subsequent reinsertion steps harder, as the corona brush density increases.28 Neither of these hypotheses has been tested directly. Here we report a TR-SANS study of PS−PEP block copolymer micelle chain exchange in squalane/PEP mixtures. Adding PEP homopolymers of the same size as the corona block into a dilute PS−PEP diblock micelle solution can introduce a controlled degree of corona overlap, while maintaining the Flory−Huggins interaction parameter between core blocks and matrix approximately constant. This mimics the situation in a more concentrated diblock or triblock micelle solution. Since adding PEP homopolymer induces corona chain overlap, it could also bring depletion interactions into play, which could cause phase separation, and possible micelle size change, as observed when polystyrene homopolymers were added into poly(styreneb-isoprene) diblock copolymer micelles in diethyl phthalate.27 Therefore, in this study we carefully monitored this potential complication using light scattering and small-angle X-ray scattering.

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EXPERIMENTAL SECTION

Materials. All chemicals were purchased from Sigma-Aldrich unless otherwise noted. The PS−PEP copolymers were synthesized as previously described, where a sequential anionic polymerization of styrene and isoprene was performed, followed by the selective saturation of the predominantly 1,4-poly(isoprene) to produce the PEP blocks.29 The deuterated equivalent d-PS−PEP copolymers were prepared in the same way using perdeuterated styrene (Polymer Source, Inc.) and normal isoprene monomers. A PEP homopolymer was prepared by anionic polymerization of isoprene in cyclohexane at 40 °C, using secbutyllithium as the initiator. The isoprene monomer was degassed and purified by mixing with n-butyllithium at 0 °C for 2 h before use. The cyclohexane solvent was purified by passing through an alumina column and bubbled with Ar to remove dissolved air. The isoprene was polymerized for 6−8 h and then terminated with degassed methanol. The resultant polymer was precipitated by adding the solution slowly into a large amount (1:3) of etamthanol. The poly(isoprene) was subsequently saturated over a Pt−Re/SiO2 catalyst (provided by Dow Chemical). A 0.02 g/mL solution of poly(isoprene) in cyclohexane was prepared, and 1 g of catalyst was added per 5 g of polymer. The reaction was performed in a sealed stainless steel reactor charged with highpressure D2 (∼500 psi) at 170 °C for 24 h with continuous stirring. The solution was then cooled, the catalyst removed by filtration, and the polymer recovered by precipitation in methanol, followed by drying in a vacuum oven at room temperature. According to 1H NMR spectroscopy, the resulting polymer is fully saturated (>99%), and the average number of deuterons per repeat unit is determined to be 2.5 due to slight H/D exchange.30−32 The molecular weight of PEP was determined using size exclusion chromatography (SEC) with a light scattering detector (Wyatt DAWN). The molecular weight and composition of the PS−PEP copolymers were determined using a combination of SEC and 1H NMR spectroscopy, as described by Choi et al.29 Table 1 summarizes the molecular weights, compositions, and dispersities Đ of the PEP homopolymer and d-/h-PS−PEP diblock copolymers.21 The PEP was designed to have the same molecular weight as the PEP block in PS− PEP diblocks, so that the overlapping of PEP chains induced by adding PEP homopolymers is comparable to that induced by increasing the concentration of PS−PEP in solution.

Figure 1. Chain exchange between deuterated (red core) and normal (blue core) PS−PEP micelles in squalane and PEP. Figure 1 illustrates the chain exchange of dilute PS−PEP micelles in squalane and PEP. Equivalent amounts of micelles composed of normal (blue core, h-PS−PEP) and deuterated (red core, d-PS−PEP) diblock copolymers are mixed. The PEP corona blocks are represented by the dark green lines, while the lighter green lines are PEP homopolymers. The purple matrix contains 58 vol % d-squalane and 42 vol % h-squalane to match the scattering length density ρ of a 50/50 hPS/dPS mixed micelle core: ρsqualane = (ρd,core + ρh,core)/2. Therefore, the exchange of isotopically labeled chains decreases the mean contrast of the micelle cores and subsequently leads to time-dependent scattering intensity. The figure schematically describes the change of corona chain concentration upon adding homopolymers of the same size as the corona blocks due to partial penetration of homopolymer into the corona. This allows examination of the impact of corona chain overlapping/stretching on the chain exchange rate. The SANS experiments were performed on the NG-7 30 m beamline at the Center for Neutron Research of the National Institute of Standards and Technology (NIST) or on the CG-2 General-Purpose SANS instrument at the High Flux Isotope Reactor (HFIR) facility at the Oak Ridge National Laboratory (ORNL). For NG-7 at NIST, a sample-to-detector distance (SDD) of 13 m and a wavelength λ = 7 Å were used. For CG-2 at ORNL, SDD = 14 m and λ = 4.75 Å. For both

Table 1. Polymer Characteristics d-PS−PEPa h-PS−PEPa PEP a

MPS (kDa)

MPEP (kDa)

Đ

29 26

71 70 64.7

1.10 1.04 1.07

Reproduced from Choi et al.21 B

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Macromolecules instruments, sample solutions were loaded into quartz cells of 1 mm thickness at room temperature. 2-D SANS data were reduced and placed on an absolute scale, using the packages provided by NIST34 and ORNL, respectively. The 99PEP samples were sandwiched between two quartz discs, confined with an aluminum washer, and sealed with a silicon-based adhesive. The sample holders were preheated to a designated temperature with a precision temperature controller (±0.2 °C) prior to the experiment. After inserting the sample cell into the heated holders, it took approximately 10 min for thermal equilibration. The temperature inside the cell was monitored by a calibrated thermocouple, with its tip inserted into a reference cell loaded with squalane and seated adjacent to the sample cell. SANS intensity was monitored at 5 min intervals for up to 3−4 h at a fixed temperature for each postmixed sample. The scattering at infinite mixing time is approximated by a premixed specimen containing micelles of 50/50 h-PS−PEP/d-PS− PEP, thus making the average scattering length density of the micelle cores matched to the solvent. These premixed micelle solutions were prepared by codissolving d- and h-PS−PEP in the micelle preparation step, followed by the same sequence of PEP addition and thermal annealing as discussed above. Small-Angle X-ray Scattering. The SAXS experiments were conducted on the equipment maintained by the DuPont−Northwestern−Dow Collaborative Access Team at Argonne National Laboratory, using 4 keV radiation (wavelength λ = 0.886 Å) and a sample-to-detector distance of 6 m. The sample solutions were loaded into quartz capillaries of approximately 1.5 mm in diameter. Each sample was exposed to the X-ray beam for 10−15 s at room temperature. The data were collected with a 2-D MAR-CCD detector and azimuthally averaged to provide the 1-D intensity profile. Background scattering from squalane was subtracted using the Irena package provided by Argonne.35 Five samples were prepared and measured: (1) the 7PEP postmixed SANS sample directly used, i.e., the PEP was added into PS−PEP micelle solutions and stirred until dissolved, with no additional thermal annealing; (2) sample 1 after annealing at 84 °C for 180 min; (3) sample 1 after annealing at 100 °C for 170 min; (4) sample 1 after annealing at 119 °C for 60 min; (5) sample 1 after annealing at 180 °C for 30 min to reach equilibrium.29 SAXS and SANS Fitting Models. Micelle structural features were extracted from the SAXS and SANS results using the Igor package provided by NIST.34 A hard sphere model with a distribution of micelle core radii, and the Percus−Yevick closure approximation in the structure factor, has been successfully used in our previous studies and documented in detail before.22,25,29 All SAXS data were fitted using this model for 0.01 Å−1 < q < 0.15 Å−1, where the wave vector q = 4πλ−1 sin(θ/2). For the TR-SANS experiment, equal amounts of d- and h-micelles are mixed in the contrast matching solvent, and as a consequence, the original form of the hard sphere model reduces to a simpler equation. Assuming a perfect contrast match is achieved (i.e., the scattering length density of the solvent is exactly the mean of d- and h-micelles cores: ρsqualane = (ρd,core + ρh,core)/2) with negligible corona scattering, and that the h- and d-micelles are randomly distributed, using the hard sphere fitting model, the coherent scattering cross section for a postmixed micelle solution can be expressed as22

⎞ dΣ(q) ⎛ 4π = ⎜ R core 3⎟ϕs(ρcore − ρsol )2 Ps(q) ⎝ 3 ⎠ dΩ

vol % PS−PEP + 3 vol % PEP, and (3) 1 vol % PS−PEP + 10 vol % PEP. For all three, the PEP was added to the diblock micelle solution at room temperature. The sample solutions were loaded into glass tubes of 1 cm diameter and degassed before taking measurements.

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RESULTS TR-SANS. Representative SANS results of postmixed 2PEP, 7PEP, and 15PEP specimens are shown in Figure 2. Each panel shows a selected set of intensity traces at various chain exchange times for one postmixed specimen at a fixed temperature. In each panel, the mixed core scattering from a corresponding premixed sample and the background scattering from a corresponding solvent (i.e., squalane for the 2PEP, 7PEP, and 15PEP specimen, PEP homopolymers for the 99PEP specimen) are included for comparison. The unmixed core scattering was measured with the postmixed sample at room temperature. The sample cell was then removed and put back in the preheated sample holder to measure the scattering intensity at 5 min intervals for up to 3−4 h. The mixed core scattering corresponds to a premixed sample and was also measured at room temperature. The systematic drop of scattering intensity is a direct consequence of redistribution of d- and h-PS−PEP between micelles. As shown in Figure 2d, the mixed core scattering from a premixed 99PEP specimen is higher than from the premixed 2PEP, 7PEP, or 15PEP specimens due to the mismatch of the PEP homopolymer scattering length density with the 50/50 mixed h/d-PS micelle cores. The open pink triangles in Figure 2d correspond to the scattering pattern of a postmixed 99PEP specimen recorded after 3 h annealing at 200 °C. This specimen was then taken out, cooled down, and remeasured at room temperature, and the corresponding scattering pattern is shown in Figure 2d. The difference between this new measurement (the green filled circles) and the previous one at 200 °C (the open pink triangles) is a result of the decreased incoherent scattering due to thermal expansion in the specimen.36 Comparing the green and red filled circles in Figure 2d, which correspond to the scattering intensity measured at room temperature using a postmixed specimen annealed at 200 °C for 3 h and a postmixed specimen before annealing, it can be concluded that within experimental uncertainty no chain exchange occurred for the 99PEP samples at 200 °C for up to 3 h. Changes in the SANS intensity were monitored as a function of time at constant temperature over the range 0.01 Å−1 ≤ q ≤ 0.04 Å−1. This q range was chosen to minimize the interference from residual corona scattering while retaining sufficient counting statistics. The extent of chain exchange as a function of time at a certain temperature can be quantitatively evaluated by the relaxation function:15 ⎡ I(t ) − I(∞) ⎤1/2 R (t ) = ⎢ ⎥ ⎣ I(0) − I(∞) ⎦

(1)

where Rcore is the core radius, ϕs is the volume fraction of hard spheres, and Ps(q) is the spherical form factor:

⎡ 3(sin(qR ) − qR cos(qR )) ⎤2 core core core ⎥ Ps(q) = ⎢ (qR core)3 ⎣ ⎦

(3)

where I(0) and I(t) represent the (integrated) initial scattered intensity and that recorded at elapsed time t of a postmixed specimen, and I(∞) is the scattering intensity at infinite time, as approximated by the premixed specimen. R(t) of 2PEP, 7PEP, and 15PEP are summarized in Figure 3. As mentioned above, no chain exchange was observed for 99PEP specimens, for up to 3 h at 200 °C. Since by this definition R(t) is independent of q, the use of R(t) to describe chain exchange relies on the assumption that micelle structure does not change over time throughout the experiment. Upon adding PEP homopolymer, however, micelles at equilibrium are expected to have a larger aggregation number

(2)

Equation 2 was used to fit the SANS data from postmixed 2PEP and 99PEP samples. Light Scattering (LS). Light scattering experiments were performed at room temperature over a range of angles (60°−120°) with a Brookhaven BI-200SM goniometer with λ = 637 nm. Three types of micelle solutions in squalane were prepared: (1) 1 vol % PS−PEP, (2) 1 C

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Figure 3. R(t,T) traces determined by TR-SANS using eq 3, with (a) 2PEP, (b) 7PEP, and (c) 15 PEP at various temperatures.

SAXS at selected temperatures used in TR-SANS chain exchange experiments, as discussed below. For each of the three samples 2PEP, 7PEP, and 15PEP, the R(t,T) obtained at different temperatures were shifted horizontally to construct a master curve, i.e., R(t/aT,Tref) = R(t,T), where the reference temperature Tref = 110 °C. This application of time−temperature superposition, which is wellknown in rheology,38,39 has been successfully exploited in all our previous studies of chain exchange.21−25 The shift factors aT were determined empirically, and log(aT) in general follows an approximately linear dependence on temperature, regardless of the concentration of PEP and PS−PEP; the shift factors are numerically consistent with previous studies (see Figure S1 in the Supporting Information for a summary plot of shift factors vs temperature for all our PS−PEP chain exchange studies). Figure 4 compares the three master curves obtained here with model fits22 of the previously reported relaxation functions for 1 vol % PS−PEP and 15 vol % PS−PEP in pure squalane. As discussed above, no chain exchange was observed with the 99PEP postmixed specimen at 200 °C for up to 3 h. Assuming the shift factor for 99PEP chain exchange follows the same dependence on temperature, this result corresponds to an R(t) value of 1 when t ≈ 3 × 1010 min and is shown in Figure 4 with the red star after the axis break.

Figure 2. Representative TR-SANS patterns recorded in 5 min increments during molecular exchange of (a) postmixed 2PEP at 100 °C, (b) postmixed 7PEP at 110 °C, (c) postmixed 15PEP at 120 °C, and (d) postmixed 99PEP at 200 °C.

than in the absence of homopolymer due to the screening of corona overlap. Therefore, micelles may have a tendency to increase in size when sufficient chain exchange is allowed. As predicted by Aniansson and Wall,37 and later elaborated for the macromolecular case by Halperin and Alexander,26 the relaxation time constant for single chain exchange at the equilibrium size should be much smaller than that for micelle size equilibration. We therefore monitored the micelle size evolution over time by D

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noticeable increase in micelle core size upon annealing at 119 °C for 60 min or 180 °C for 30 min, which correspond to the last purple point in Figures 3b and 4 and the premixed sample measured in SANS, respectively. The SAXS pattern of sample 3 (pink) falls between samples 2 (blue) and 4 (purple), indicating a modest increase in micelle core radius, which corresponds to the last dark yellow point (100 °C) in Figures 3b and 4. The fitted mean core radii of samples 1, 2, 3, 4, and 5 are 92, 92, 96, 103, and 105 Å, respectively, with a distribution width of less than 10% and a fitting uncertainty of less than 2%. The fitted core radius of sample 1 is close to the previously reported value (88 Å) for 1 vol % PS−PEP in squalane21 due to the fact that the PEP was added at room temperature where the PS cores were frozen. As a comparison, according to Choi et al.,29 for both 0.5 and 1 wt % PS−PEP micelle solutions in pure squalane, both the size of the micelle cores and the hydrodynamic radius of the micelles increased by about 10% when heated to around 180 °C. When cooled back down to room temperature, however, both values were recovered. Therefore, the presence of PEP homopolymers contributes to the observed irreversible change in micelle size in these 7PEP specimens. SANS Fitting. The SANS data from a postmixed 2PEP (red open squares) and 99PEP (blue open circles) taken at room temperature before chain exchange were fit using eq 1 to find the mean core radius, and the fitting results are compared with the data in Figure 6. The results suggest a significant increase in

Figure 4. R(t) or R(t/aT,Tref) master curves for (left to right) 2PEP, 7PEP, and 15PEP at a reference temperature 110 °C. The lines are model fits of 1 vol % (left, blue) and 15 vol % (right, red) PS−PEP in pure squalane.22 The red star corresponds to the 200 °C measurement with postmixed 99PEP for 3 h, where no chain exchange was observed.

SAXS. The SAXS data for five 7PEP samples after different thermal treatments are plotted with corresponding fitting curves in Figure 5. (These date are also replotted in Figure S2 by shifting

Figure 5. SAXS of five 7PEP solutions measured at room temperature: before any annealing (sample 1, black), after 180 min annealing at 84 °C (sample 2, blue), after 170 min annealing at 100 °C (sample 3, pink), after 60 min annealing at 119 °C (sample 4, purple), and after 30 min annealing at 180 °C (sample 5, red). The open circles are data corresponding to the five samples, as denoted in the legend. The solid lines of the same color are fitting curves for each.

Figure 6. SANS data and fitting of postmixed 2PEP (red) and 99PEP (blue) using eq 1. The open symbols are SANS data, and the lines of the same color are fitting curves. The fitted core radii Rcore are shown in the plot.

micelle core radius upon switching the solvent from squalane to PEP. In addition, the fitted core radius for postmixed 2PEP from eq 1 is close to that from a complete core−shell hard sphere fitting model22 fit to SAXS data from a postmixed 7PEP specimen (Figure 5). Both these two fitted core radii are consistent with the reported value for 1 wt % PS−PEP in pure squalane.29 As a comparison, the unperturbed radius of gyration ⟨Rg⟩0 of the PS core block to the core radius can be estimated as 44 Å from the reported value of 6⟨Rg2⟩0/MW (0.434 for PS at 413 K40). Therefore, our SANS and SAXS fitting results suggest that the core blocks are not significantly stretched. And, as the experimental value is at least twice ⟨Rg⟩0, the core sizes estimated from fittings are entirely reasonable. Since the PEP was added in both 2PEP and 7PEP at room temperature when the PS cores are frozen, 39 the two values should be the same if the aforementioned assumptions of deducing eq 1 are satisfied. Therefore, the fact that the SANS and SAXS fitting results of the

each set vertically for a clearer view of the data points and corresponding fits.) Samples 1−5 correspond to 7PEP micelle solutions with no thermal annealing and after annealing at 84 °C for 180 min, at 100 °C for 170 min, at 119 °C for 60 min, and at 180 °C for 30 min, respectively. Therefore, sample 1 corresponds to the initial micelles in a TR-SANS experiment before any chain exchange takes place, while samples 2−4 represent the last data points in the TR-SANS traces acquired at each corresponding temperature, and sample 5 is comparable to the premixed sample used in SANS. The SAXS patterns of samples 1 (black) and 2 (blue) overlap with each other within experimental error, implying that no micelle size change occurs at 84 °C for up to 3 h, which corresponds to the longest time data point in the SANS results presented in Figures 3 and 4 for 7PEP at 84 °C (i.e., the last light gray point in Figures 3b and 4). The SAXS patterns of samples 4 (purple) and 5 (red), on the other hand, suggest a E

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authors showed by off-lattice Monte Carlo simulations that compared to small molecule solvents of identical chemical species, a polymer chain has reduced free volume due to bonding constraints, which consequentially leads to a positive contribution to the entropy of mixing. Therefore, by substituting part of the solvent squalane with PEP, the χ between PS and the matrix should decrease slightly, and the chain exchange process should be mildly facilitated, if the core enthalpic expulsion energy penalty (∼χ) is the only obstacle each chain experiences when leaving a micelle. Clearly, this effect is opposite to the observed slower kinetics in 7PEP, 15PEP, and 99PEP micelle solutions. Three possible explanations for this discrepancy are herein considered: (1) the increase of diffusion time of free chains, due to increased matrix viscosity; (2) the possibility of a larger barrier for a core block to enter the corona region, due to the increased micelle size (and resulting corona crowding) induced by the presence of PEP, as proposed by Halperin;28 (3) a reduction in a favorable corona contribution to the total chain expulsion activation energy, i.e., the relief of stretching of corona blocks upon escaping from a micelle, which favors free chains, is partially screened by the presence of PEP homopolymers. The last of these is found to be the major contribution. 1. Matrix Viscosity. First, we estimate the effect of adding PEP homopolymer on single chain diffusion. As shown in Figure 4, the 2PEP exhibits a chain exchange rate that is comparable to the one without PEP (1 vol % PS−PEP in squalane, blue line). The viscosity of the solvent (squalane + 1 vol % PEP) can be estimated as ηs ≈ ηsqualane(1 + [η]c). Since squalane is chemically very similar to PEP, the intrinsic viscosity of PEP in squalane can be estimated using the Mark−Houwink equation as [η] = KM1/2. The value of K is in general below 0.5 (mL/g)1/2 for PEP in various theta solvents,45 which is used as a rough estimation. Therefore, the viscosity of solvent with the addition of 2 vol % PEP can be estimated as 6.6 mPa·s, given that the viscosity of squalane is about 2.2 mPa·s at 100 °C.46 The fact that increasing the solution viscosity by 3 times does not change the chain exchange rate thus suggests that the solution viscosity is not the rate-limiting step, as expected.24,26 This inference is also supported by an approximate comparison of the time constant for the expulsion of core blocks from one micelle, with the (much shorter) characteristic time for a polymer chain to diffuse from one micelle to another, as discussed in more detail in the Supporting Information. 2. Core Size Evolution. Second, we consider changes in micelle aggregation number due to the effect of adding homopolymers, which could possibly impact both the initial step (core block entering the corona) and the last step in a unimer exchange mechanism, i.e., the reinsertion of a unimer into a micelle. According to Halperin,28 the rate of chain exchange decreases when the micelle core size is larger due to an increased barrier for the core blocks to enter the corona. Since the PEP homopolymers were added into dilute PS−PEP micelle solutions at room temperature for the 2PEP, 7PEP, and 15PEP samples prepared for TR-SANS, the initial micelle sizes in these samples were the same as in dilute PS−PEP/squalane solutions. Only after sufficient chain exchange at an elevated temperature can the micelles grow in order to achieve the larger equilibrated size due to the presence of PEP. During TR-SANS, the micelle solutions were heated to around 100 °C and allowed to reach the equilibrated structure gradually. The equilibrium size of the micelles increases with adding corona homopolymer due to corona overlap22,27 and thus will possibly increase the energy barrier for chain insertion.28 Therefore, there could be the

postmixed solutions match suggests the successful use of contrast matching and that the d/h-micelles are randomly mixed. We attribute the modest departure of the data from the model fit for q < 0.02 Å−1 in Figure 6 to excess corona scattering and slight contrast mismatch due to the addition of PEP.

Figure 7. Mean-square scattering intensity square measured at different angles for three micelle solutions in squalane, as denoted by the legend.

Light Scattering. The mean-square scattering intensity ⟨Iave⟩2, directly measured on the DLS instrument, serves as a qualitative evaluation of whether depletion-induced phase separation occurs due to the addition of PEP homopolymer. Figure 7 summarizes the ⟨Iave⟩2 × sin2 θ measured at various angles θ for three micelle solutions with the same PS−PEP concentration, but differing PEP content. Here the squared intensity is corrected by sin2 θ due to the fact that the scattering volume at different detecting angles varies by sin−1 θ. All scattering intensities are in units of total photon counts measured by the detector. The fact that the intensity is essentially angle independent in all cases is strong evidence that there is no appreciable tendency of the micelles to aggregate or phase separate in the presence of the homopolymer.

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DISCUSSION The first and most important observation from Figure 4 is that the chain exchange rate decreases significantly with the addition of PEP homopolymer (three master curves from left to right). Furthermore, the magnitude of the slowing down is comparable to the reported slower kinetics in body-centered cubic ordered 15 vol % PS−PEP solutions. The model for R(t) proposed by Choi et al.,21 which successfully fit the chain exchange data for several diblocks, cannot explain this result. In this model, R(t) is based on the assumptions that single chain expulsion is the ratelimiting step and that the activation energy of chain exchange is solely governed by the interaction between the core blocks and the corona/solvent matrix. The rate is strongly dependent on core block length, but the corona is not explicitly considered. It is well-known that the Flory−Huggins interaction parameter χ for a polymer/solvent system is often larger than χ for a polymer/ polymer blend, where the second polymer has the same repeat unit structure as the solvent.41,42 In the current system, squalane is essentially a PEP hexamer. While χ for a polymer/polymer system can often be as low as 10−2−10−3, empirically it is found that χ for many polymers even in good solvents tends to a lower limit of about 0.34.41−43 Milner and co-workers examined the χ of polyethylene in 17 n-alkanes, where χ decreases as n, the number of carbon atoms in one alkane molecule, increases.44 The F

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Macromolecules

⎡ R 3/2(ϕ = 0) ⎛ R 3/2(ϕ ) ⎞⎤ core core A A ⎜⎜ ⎟⎟⎥ ≈ exp⎢ − − 1 3/2 ⎢⎣ kex(ϕA = 0) NB1/2a3/2 ⎝ R core (ϕA = 0) ⎠⎥⎦ (7)

complication of an increasing micelle size during the course of the chain exchange experiments. We assessed this issue by separately annealing the h- and dmicelle solutions at 180 °C for 30 min after adding PEP but before postmixing (see Figure 5 for SAXS data and fits). With those “preannealed” samples, the chain exchange rates did not change within experimental error, while the core radius of the micelles did change by approximately 10% (92 Å to 105 Å for 7PEP). Therefore, as shown in Figure 4, the chain exchange rate of 1 vol % PS−PEP micelles in pure squalane is about 10 times faster than that of 7PEP, while the micelle sizes remain constant during both chain exchange processes. A comparison can thus be made between this result and Halperin’s analysis.28 According to the latter, the chain exchange for diblock micelles in mixtures of a small molecule selective solvent and homopolymers of the same kind and size as the corona blocks could experience a larger chain insertion barrier ΔFins, when the core block enters the corona region in the chain extraction step, which leads to slower exchange compared to diblock micelles of the same concentration in pure solvent. As a result, the ratio of the chain exchange rate constant kex of 7PEP (volume fraction of PEP ϕA = 7%, with A being PEP and B being the PS core block) to that of 0PEP (i.e., 1 vol % PS−PEP in pure squalane, ϕA = 0) can be expressed as28 kex(ϕA ) kex(ϕA = 0)

≈ exp{−[Fa(ϕA ) − Fa(ϕA = 0)]}/kT

kex(ϕA )

Since for 2PEP, 7PEP, and 15PEP the PEP was added in diblock micelle solutions and not annealed afterward, Rcore(ϕA = 0) can be estimated to be 92 Å (Figure 5). Using the value of NB from Table 1, a = 2.52 Å as estimated by the length of two C−C bonds, Rcore(ϕA = 0) = 92 Å and Rcore(ϕA = 7%) = 105 Å, eq 7 gives the ratio of kex(ϕA = 7%)/kex(ϕA = 0) ≈ 0.05. This analysis suggests a slightly larger retardation effect upon adding PEP homopolymers compared to the experimental value of kex(ϕA = 7%)/kex(ϕA = 0) ≈ 0.1 (Figure 4). To further investigate the core size evolution during SANS experiments, a postmixed 7PEP specimen was annealed at 84 °C for 3 h (the same temperature and time as the first R(t) trace of 7PEP in Figures 4 and 3) and subsequently analyzed by SAXS to quantify any change in micelle size in the corresponding SANS experiment. As shown in Figure 5, the thermal annealing at 84 °C does not introduce any noticeable change in micelle size. However, SAXS of two more postmixed 7PEP specimen annealed at higher temperatures (100 °C for 170 min and 119 °C for 60 min; see Figure 5) suggests that the core radius of the micelles is gradually increasing (to 98 and 103 Å, correspondingly) when chain exchange is more significant. In other words, while the chain exchange rate of 7PEP at 84 °C is not affected by any micelle core size change, the micelles do have a tendency to gradually increase their mean aggregation number at higher temperatures (100 °C and above) during the TR-SANS experiments. Therefore, we can conclude that adding PEP homopolymers into dilute PS−PEP micelle solutions can retard chain exchange rate even when the micelle size remains the same (i.e., at relatively low temperatures such as 84 and 90 °C for up to 3 h). But because the separately annealed 7PEP micelles with a larger size (105 Å compared to the original 92 Å) possess identical chain exchange rates within experimental error, we conclude that the micelle size change due to added homopolymer is not the primary contributing factor to the results presented here. 3. Corona Screening. Third, we discuss the screening of corona chain stretching due to the corona overlap in added PEP samples. As shown in Figure 4, chain exchanges of 7PEP and 15PEP solutions are both slower than without PEP. Similar slower kinetics as a result of increasing concentration of PS−PEP from 1 to 15 vol % has been observed and attributed to the screening effect of overlapping coronas.22 The critical volume fraction for added PEP homopolymers to overlap with PEP coronas can be estimated as the volume fraction of PEP blocks inside the corona: ϕ* = (Nagg × Vcorona)/(4/3 × π × (Rhs3 − Rc3)). For the PS−PEP polymers used in the study, the occupied volume of a corona block, i.e., the total volume of a corona chain made of Ncorona repeat units, Vcorona = Ncorona × Vcorona_0 ≈ 136 000 Å3, where Ncorona is the number of repeat units in one corona chain and Vcorona_0 is the volume of one repeat unit in the corona chain, estimated using the bulk density of PEP, assuming the density is the same as that for PEP bulk homopolymers. The values of aggregation number Nagg, hard sphere radius estimated from SAXS fittings Rhs, and core radius Rc were reported for 1 vol % PS−PEP solution in squalane at 100 °C to be Nagg ≈ 70, Rhs ≈ 362 Å, and Rc ≈ 88 Å.29 Therefore, the overlap volume fraction of PEP in 1 vol % PS−PEP is approximately 5 vol %. Based on this calculation, there is little corona overlap in 2PEP but significant overlap in 7PEP and 15PEP, consistent with the observation that

(4a)

where Fa(ϕA) is the activation free energy of extracting core blocks from micelle cores. Fa(ϕA) is determined by two aspects of chain extraction: the change of free energy due to the change in chemical environment for the core block when it enters the corona/solvent matrix and the change of the micellar free energy due to the creation of a core block “bud” when entering the corona region. Since the solvent (squalane) is essentially a low molecular weight version of the homopolymer (PEP), the first component of Fa(ϕA) is assumed to be unaffected by ϕA. The second component of Fa(ϕA), according to Halperin, comes from the work of inserting an impenetrable particle against the osmotic pressure of the coronal, ΔFins. Therefore, eq 4a becomes kex(ϕA ) kex(ϕA = 0)

≈ exp{−[Fins(ϕA ) − Fins(ϕA = 0)]}/kT (4b)

where ΔFins(ϕA = 0) ≈ kTR core 3/2(ϕA = 0)/NB1/2a3/2

(5)

and ΔFins(ϕA ) ≈ kTR core 3/2(ϕA )/NB1/2a3/2 , when ϕ* > >ϕA > >ϕ**

(6)

where NB is the number of repeat units in a PS block, Rcore is the micelle core radius, and a is the size of one monomer. Here ϕ* is the threshold volume fraction of PEP homopolymers, above which the PEP homopolymer chains overlap with PEP coronas. ϕ* is estimated as 5 vol %, as discussed below. ϕ** is the critical volume fraction of PEP homopolymers added to introduce screening in the entire corona region, and the whole coronal star structure disappears as a consequence. Therefore, ϕA = 7% falls in between the two limits, and eqs 4a and 4b become G

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Macromolecules there is no chain exchange rate reduction with 2PEP but significant reduction in 7PEP and 15PEP. The SAXS experiments by Choi et al. suggest slight chain stretching (Rg/⟨Rg⟩0 ≈ 1.4) in the PEP corona blocks in 1 wt % PS−PEP micelle solutions in squalane.29 Both our chain exchange study with triblock PEP−PS−PEP in squalane25 and Halperin’s earlier theoretical work26 imply a facilitating role of corona blocks in chain exchange. In pure squalane, the corona chains experience a relief of stretching by escaping into a good solvent. Either when the coronas are partially penetrated by homopolymers of the same size or when they overlap due to increased concentration of PS−PEP, PEP corona blocks remain in semidilute solution whether or not they are part of a micelle. Therefore, the observed slower kinetics upon adding PEP to above ϕ* is predominantly a result of the screening effect; i.e., the benefit to the corona block to escape the micelle is reduced compared to in dilute solution. While consideration of the corona blocks can provide a qualitative explanation for the main feature in Figure 4, it should be noted that at early reduced times the R(t) master curves of 7PEP and 15PEP do not follow exactly the model fits of 1 or 15 vol % PS−PEP micelles in pure squalane (the red and blue lines of Figure 4): the initial chain exchange rate seems to be greater than the model prediction. The reason for this observation is not yet clear. The possibility of micelle aggregation accelerating chain exchange in certain regions due to the depletion effect of added PEP in PS−PEP solutions27 can be excluded by visually checking the solutions (always optically clear) and by measuring the light scattering intensity as a function of added homopolymer. Since even the scattering intensity of the solution containing 10 vol % PEP is not greatly different from the one without PEP at any detector angle (Figure 7), we conclude that any micelle aggregation is very mild and certainly that no macrophase separation occurs upon adding PEP up to at least 10 vol %. Chain Exchange of PS−PEP in Pure PEP Homopolymer. Chain exchange in 99PEP (1 vol % PS−PEP + 99 vol % PEP) is extremely slow and not detectable at 200 °C for up to 3 h in the TR-SANS experiment. This result is consistent with 7PEP and 15PEP in the sense that added PEP slows down the chain exchange, and it is also not predicted in the previous model that only considers the core block expulsion activation energy,21 as discussed above. However, even though in 99PEP specimens the corona contribution in chain exchange is completely screened, the extreme slow kinetics may not be fully explained if only corona chain overlap is considered. In addition to the corona block effect, here we consider another possibility: an increased activation energy for core blocks to enter the corona region, in both the chain extraction and reinsertion steps.28 As shown in Figure 6, the 1 vol % PS−PEP micelles in pure PEP are much larger than those in squalane (core radius of 159 Å compared to 92 Å), as can be expected from the increased screening effect of PEP. This significantly increases the brush density of the PEP corona blocks. As discussed above, Halperin’s theoretical work suggests that the substitution of the solvent with homopolymers of the same kind and size as the corona blocks could lead to a larger chain insertion barrier ΔFins and thus to slower chain exchange rates. In the case of 99PEP, ϕA = 99% > ϕ**, and ΔFins is determined by the bulk osmotic pressure instead:28 ΔFins(ϕA ) ≈ kTNBϕA 9/4

kex(ϕA ) kex(ϕA = 0)

≈ exp[R core 3/2(ϕA = 0)/NB1/2a3/2

− NBϕA 9/4],

for ϕA = 99% > ϕ**

(9)

Using the value of NB from Table 1, a = 2.52 Å, Rcore (ϕA = 0) = 92 Å, and Rcore (ϕA = 99%) = 159 Å, eq 9 gives the ratio of kex(ϕA = 99%)/kex(ϕA = 0) < exp(−200). Therefore, in addition to the profound screening of corona chain stretching by added PEP, having such a large micelle in PEP could also significantly increase the chain insertion energy barrier, both of which would contribute to a much slower chain exchange rate. One further issue to consider is the evolution of the dependence on χ in the activation energy term for core block extraction, which was expressed as αχN in the model proposed by Choi et al.,21 where χ is the interaction parameter between core blocks and the solvent/homopolymer matrix, N is the number of repeat units in a core block, and α is an O(1) constant. In a melt, this expression describes the interaction between the core blocks and the homopolymer matrix. However, for micelles in solution, another expression should be used instead, possibly α(χ − 0.5)N, as χ must be larger than 0.5 for the formation of micelles. This difference in the dependence on χ during the gradual transition from a dilute solution to a melt upon adding PEP homopolymer might also contribute to the dependence on PEP concentration observed in this study.

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SUMMARY

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ASSOCIATED CONTENT

The chain exchange in 1 vol % diblock copolymer PS−PEP micelles in squalane and with varying amounts of added PEP homopolymer has been investigated using TR-SANS. The micelle structure was characterized by SANS and SAXS with appropriate fitting models. The results suggest that the addition of PEP retards chain exchange only when in sufficient quantity to partially penetrate into the corona region (i.e., when ρPEP > ρ* ≈ 5 vol %), consistent with an earlier study of concentrated diblock micelle solutions.22 The more PEP is added, the slower the chain exchange rate becomes; in the limit where the solvent is completely replaced by PEP homopolymer, the chain exchange becomes too slow to be detected, even at substantially elevated temperatures. The influence of both the screening of corona chain stretching and the increasing in micelle core size due to PEP addition are discussed. We herein propose that the relief of corona block stretching upon escaping from a micelle favors chain expulsion from one micelle in dilute solution and that the reduced chain exchange rate upon adding PEP or increasing diblock concentration is primarily due to the screening effect of PEP homopolymer on PEP corona blocks. On the other hand, the chain exchange of PS−PEP micelles in pure PEP homopolymer was found to be extremely slow. While this observation is consistent with the trend found with 7PEP and 15PEP specimens where squalane was partially substituted with PEP, the significant increase in aggregation number and thus corona chain density is another contributing factor that slows down the chain exchange rate, as anticipated theoretically.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b02395.

(8)

Therefore, eqs 4a and 4b become H

DOI: 10.1021/acs.macromol.5b02395 Macromolecules XXXX, XXX, XXX−XXX

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(17) Lund, R.; Willner, L.; Lindner, P.; Richter, D. Macromolecules 2009, 42, 2686−2695. (18) Lund, R.; Willner, L.; Pipich, V.; Grillo, I.; Lindner, P.; Colmenero, J.; Richter, D. Macromolecules 2011, 44, 6145−6154. (19) Zinn, T.; Willner, L.; Lund, R.; Pipich, V.; Richter, D. Soft Matter 2012, 8, 623−626. (20) Lund, R.; Willner, L.; Richter, D. Adv. Polym. Sci. 2013, 259, 51− 158. (21) Choi, S.-H.; Lodge, T. P.; Bates, F. S. Phys. Rev. Lett. 2010, 104, 047802. (22) Choi, S.-H.; Bates, F. S.; Lodge, T. P. Macromolecules 2011, 44, 3594−3604. (23) Lu, J.; Choi, S.; Bates, F. S.; Lodge, T. P. ACS Macro Lett. 2012, 1, 982−985. (24) Lu, J.; Bates, F. S.; Lodge, T. P. ACS Macro Lett. 2013, 2, 451−455. (25) Lu, J.; Bates, F. S.; Lodge, T. P. Macromolecules 2015, 48, 2667− 2676. (26) Halperin, A.; Alexander, S. Macromolecules 1989, 22, 2403−2412. (27) Abbas, S.; Lodge, T. P. Phys. Rev. Lett. 2007, 99, 137802. (28) Halperin, A. Macromolecules 2011, 44, 5072−5074. (29) Choi, S.-H.; Bates, F. S.; Lodge, T. P. J. Phys. Chem. B 2009, 113, 13840−13848. (30) Habersberger, B. M.; Lodge, T. P.; Bates, F. S. Macromolecules 2012, 45, 7778−7782. (31) Nicholson, J. C.; Crist, B. Macromolecules 1989, 22, 1704−1708. (32) Tanzer, J. D.; Crist, B. Macromolecules 1985, 18, 1291−1294. (33) Lai, C.; Russel, W. B.; Register, R. A. Macromolecules 2002, 35, 841−849. (34) Kline, S. R. J. Appl. Crystallogr. 2006, 39, 895−900. (35) Ilavsky, J.; Jemian, P. R. J. Appl. Crystallogr. 2009, 42, 347−353. (36) The thermal expansion coefficients of PS and PEP at 200 °C have been reported to be 5.6 × 10−4 and 7.3 × 10−4 K−1 (see ref 43). Therefore, it is plausible that the change of incoherent scattering due to thermal expansion is not q independent, with the PEP corona chains expanding more (which dominates for q ≤ 0.01 Å−1) and the PS core chains expand less, consistent with observation. (37) Aniansson, E. A. G.; Wall, S. N. J. Phys. Chem. 1975, 79, 857−858. (38) Ferry, J. D. Viscoelastic Properties of Polymers; John Wiley & Sons: 1980. (39) Williams, M. L.; Landel, R. F.; Ferry, J. D. J. Am. Chem. Soc. 1955, 77, 3701−3707. (40) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Macromolecules 1994, 27, 4639−4647. (41) Hiemenz, P. C., Lodge, T. P. Polymer Chemistry, 2nd ed.; CRC Press: 2007. (42) Brandrup, J.; Immergut, E. H.; Grulke, E. A.; Abe, A.; Bloch, D. R. Polymer Handbook; Wiley: New York, 1999; Vol. 89. (43) Mark, J. E. Physical Properties of Polymers Handbook, 2nd ed.; Springer: 1996. (44) Milner, S. T.; Lacasse, M.-D.; Graessley, W. W. Macromolecules 2009, 42, 876−886. (45) Mays, J. W.; Fetters, L. J. Macromolecules 1989, 22, 921−926. (46) Poole, C. F.; Pomaville, R. M.; Dean, T. A. Anal. Chim. Acta 1989, 225, 193−203.

shift factors log(aT) as a function of temperature, replot of Figure 5 with vertically shifted data and fitting curves, comparison of diffusion vs core extraction time constants, estimate of chain exchange in the presence of pentane (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (F.S.B.). *E-mail [email protected] (T.P.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Infineum USA, L. P. We appreciate help with the SANS experiments from Dr. Yuri Melnichenko (ORNL), Dr. Lilin He (ORNL), Dr. Paul Butler (NIST), and Dr. Matthew Wasbrough (NIST). We also acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in part of this work; some TR-SANS experiments were conducted at Oak Ridge National Laboratory’s High Flux Isotope Reactor, which is sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. This research also used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. The SAXS data were collected on the X-ray Operations and Research beamline 5-ID at the Advanced Photon Source, Argonne National Laboratory. The beamline is operated by the DuPont−Northwestern−Dow Collaborative Access Team (DND-CAT).

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REFERENCES

(1) Gohy, J. F. Adv. Polym. Sci. 2005, 190, 65. (2) Halperin, A.; Tirrell, M.; Lodge, T. P. Adv. Polym. Sci. 1992, 100, 31−71. (3) Won, Y.-Y.; Davis, H. T.; Bates, F. S. Macromolecules 2003, 36, 953−955. (4) Meli, L.; Santiago, J. M.; Lodge, T. P. Macromolecules 2010, 43, 2018−2027. (5) Jain, S.; Bates, F. S. Macromolecules 2004, 37, 1511−1523. (6) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905−922. (7) Wennerström, H.; Lindman, B. Phys. Rep. 1979, 52, 1−86. (8) Wang, Y.; Kausch, C. M.; Chun, M.; Quirk, R. P.; Mattice, W. L. Macromolecules 1995, 28, 904−911. (9) Prochazka, K.; Kiserow, D.; Ramireddy, C.; Tuzar, Z.; Munk, P.; Webber, S. E. Macromolecules 1992, 25, 454−460. (10) Smith, C. K.; Liu, G. Macromolecules 1996, 29, 2060−2067. (11) van Stam, J.; Creutz, S.; De Schryver, F. C.; Jérôme, R. Macromolecules 2000, 33, 6388−6395. (12) Underhill, R. S.; Ding, J.; Birss, V. I.; Liu, G. Macromolecules 1997, 30, 8298−8303. (13) Lund, R.; Willner, L.; Stellbrink, J.; Radulescu, A.; Richter, D. Phys. B 2004, 350, E909−E912. (14) Lund, R.; Willner, L.; Richter, D.; Dormidontova, E. E. Macromolecules 2006, 39, 4566−4575. (15) Lund, R.; Willner, L.; Stellbrink, J.; Lindner, P.; Richter, D. Phys. Rev. Lett. 2006, 96, 068302. (16) Lund, R.; Willner, L.; Richter, D.; Iatrou, H.; Hadjichristidis, N.; Lindner, P. J. Appl. Crystallogr. 2007, 40, s327−s331. I

DOI: 10.1021/acs.macromol.5b02395 Macromolecules XXXX, XXX, XXX−XXX