Multiblock Inverse-Tapered Copolymers: Glass Transition

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Multiblock Inverse-Tapered Copolymers: Glass Transition Temperatures and Dynamic Heterogeneity as a Function of Chain Architecture Jarred Kelsey, Nathan Pickering, Andrew Clough, Joe Zhou,* and Jeffery L. White* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078, United States S Supporting Information *

ABSTRACT: Systematic variation of the size and number of inverse-tapered blocks in styrene−butadiene copolymers results in a wide range of accessible glass-transition temperatures (Tg), including Tg’s approaching that predicted by the Fox equation. Composition-weighted average Tg’s are expected for miscible blends or random copolymers, but such behavior has not previously been reported for block copolymers made from immiscible styrene and butadiene segments. In this work, 50:50 wt % multiblock copolymers with Mn = 120 000 kg/mol were synthesized using an inverse-tapered block design for all blocks except the end blocks. The total composition and molecular weight were held constant, but the type and number of blocks were systematically varied in order to compare contributions from the inverse-tapered chain interfaces to the overall glass transition behavior. Discrete copolymers of similar block number and length were investigated as controls to help separate contributions from the inverse-tapered design and the molecular weight of individual blocks. Some copolymers were intentionally designed such that individual block molecular weights were between the entanglement molecular weight (Me) of polystyrene (PS) and polybutadiene (PB). A range of intermediate glass transitions was observed, but the inverse-tapered copolymers that satisfied this latter condition were the only copolymers that exhibited a Tg near a composition-weighted average. Solid state NMR reveals dynamic heterogeneity among monomeric components through chain-level identification of relatively large amounts of rigid PB segments and mobile PS chain segments versus that observed in discrete block analogues where essentially all PB segments are mobile and all PS segments are rigid. NMR revealed subtle differences in the temperature-dependent segmental chain dynamics of different inverse-tapered blocks, which were not obvious from the calorimetric studies but which presumably contribute to the longer length scale Tg behavior.

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INTRODUCTION Copolymer properties depend upon a combination of the individual monomer chemical structures, regio- and stereoisomerism in monomer enchainment, monomer sequencing, and overall phase morphology as dictated by the thermodynamics of the mixed monomer system via the product of the polymer length (N) and the Flory interaction parameter (χ).1−5 Specific copolymers with attractive physical properties over a wide temperature range, e.g., toughness, are typically designed by varying the amounts of two individual components to achieve a final material with bulk physical properties intermediate between the extremes defined by their two pure constituents. In the absence of random copolymerization of monomers with similar reactivity ratios, comonomers are most often introduced in alternating sequence leading to discrete block copolymers. Recent interest in copolymers prepared through parallel introduction of comonomers in varying but predefined amounts has led to designed gradient or tapered copolymers, as described by several experimental and theoretical investigations, and whose properties can be distinct relative to discrete block copolymers of similar composition.6−14 For example, Epps and co-workers have demonstrated that styrene−isoprene copolymers can adopt double-gyroid © XXXX American Chemical Society

morphologies, with reductions in order−disorder temperatures for tapered block copolymers relative to discrete block copolymers in both bulk samples and thin films.15−18 Hall and co-workers have shown through detailed calculations that morphologies can vary in tapered versus inverse-tapered copolymers for the same composition and that order−disorder transitions are significantly affected by the introduction of inverse-tapered chain topologies.19,20 At longer length scales, such outcomes may be similar to the effect of blending random styrene−butadiene copolymers into discrete copolymers.21 Experiments by Clough et al. showed that, compared to discrete block copolymer analogues, quantifiable amounts of butadiene chain segments are incorporated in a rigid “high-Tg” phase, and similarly styrene segments incorporated in a soft “low-Tg” phase, as part of the interfacial region of tapered and inverse-tapered styrene−butadiene copolymers.22,23 Chain dynamics, glass-transition temperatures, and morphology ultimately govern macroscopic properties, and several groups have explored similarities between these properties in gradient Received: July 11, 2017 Revised: August 28, 2017

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DOI: 10.1021/acs.macromol.7b01476 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules designs versus random or block copolymers.24−28 In the previous experimental reports mentioned above, the tapered or inverse-tapered block constituted a single central block of an effective triblock polymer chain bounded by pure discrete blocks. In this contribution, glass transition behavior in multiblock inverse-tapered styrene−butadiene copolymers is investigated and compared to multiblock discrete copolymers with identical chemical compositions and chain length. Styrene and butadiene were chosen because their individual polymer Tg’s vary by almost 200 K, and even though random copolymers of these two monomers are routinely made, general extensions of the multiblock ITB (inverse-tapered block) approach to comonomers with large differences in reactivity ratios could prove useful for new materials design. Chain-specific contributions to the observed glass transition behavior are shown to vary considerably among the inverse-tapered multiblock copolymer designs, with NMR experiments revealing chain-level dynamic heterogeneities that are not resolved in calorimetric experiments on the same materials and whose temperature dependence is a function of chain structure. Systematic variation of the size and number of inverse-tapered blocks in styrene−butadiene copolymers results in a wide range of accessible glass-transition temperatures (Tg), including composition-weighted Tg’s approaching those predicted by the Fox equation and which cannot be accessed using multiblock discrete copolymer analogues.

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inverse-tapered blocks are also shown in Scheme 1, and an example calculation for ITB-20 is given in the Supporting Information. In the nitrogen-purged reactor, 2500 g of dried cyclohexane was added by pressure and controlled mass flow meter. The reactor jacket temperature was maintained at 70 °C. An 18 mL aliquot of 0.2 g per millimeter of dried THF in cyclohexane solution was introduced by syringe. Subsequently, 200 g of styrene was added, followed by 37 g of 2% n-butyllithium in cyclohexane solution. After measuring a 2 °C temperature drop from peak temperature, 100 g of butadiene and 100 g of styrene were introduced simultaneously into the reactor. This step was repeated based on the number of desired blocks, followed by addition of 200 g of butadiene as the last step in the ITB-20 example. After consumption of the butadiene monomer as indicated by a 2 °C temperature drop, and polymerization completed, the solution was neutralized by water and CO2 followed by antioxidants. Calorimetry. Modulated differential scanning calorimetry (MDSC) measurements were done on a TA Instruments Q2000, using a liquid nitrogen cooling system (LNCS), at a helium gas flow rate of 50 mL/ min. Sapphire and indium were used as calibration standards. Samples were pressed into pellets to increase the loading weight in the “Tzero” aluminum pans to a mass of 10−15 mg. All samples were heated at a 10 K/min rate to 433 K and held for 120 min prior to quenching to 113 K. The reversing heat flow was measured using a 2.5 K/min ramp rate, with a ±1.590 K modulation every 60 s, up to 433 K. NMR Measurements. 1H and 13C solution NMR measurements were collected on a Bruker 400 MHz spectrometer, using chloroform or THF as the solvent, from which copolymer compositions and sequence effects were calculated. 1H solution data were strictly quantitative, while 13C solution data were acquired with NOE (nuclear Overhauser enhancement). Quantitative spin-counting MAS spectra using the previously published internally calibrated method22,29 were obtained at room temperature on the solid copolymers, using a Bruker Avance-400 spectrometer operating at a magnetic field strength of 9.4 T, and 6−7 kHz MAS (magic-angle spinning) speeds. Variabletemperature 1H solid-state MAS measurements were collected on a Bruker DSX-300 spectrometer operating at a magnetic field strength of 7.05 T, using a Bruker 4.0 mm triple-resonance MAS probe at 5 kHz spinning speed. Spectra were obtained using a single 90° pulse, with a 3.5 μs pulse width, a 10 μs receiver delay, and a 10 s repetition delay time (longer than 5T1H for either PS or PB), starting at 190 K and going up to 340 K in 10 K increments. Prior to the acquisition of each new temperature spectrum, the sample was equilibrated at that temperature for 10 min. Temperature was varied by flowing nitrogen gas through a heat exchanger immersed in a liquid N2 reservoir, with subsequent heating to the desired temperature inside the MAS probe. Spin-diffusion experiments were acquired using a direct-detection 1 H dipolar filter30 experiment, similar to that previously described by Molnar et al.,31 in which three cycles of the 12-pulse filter with 10, 20, or 40 μs interpulse spacings were used to select initial polarization from the most mobile (long T2) component as the source.32 Alternating parallel/antiparallel storage was used for T1 compensation, and data were collected without MAS in order to eliminate any perturbations to the spin-diffusion process as recently described by the Saalwächter group.33 Domain sizes for the polybutadiene-rich source region in the discrete block copolymers were calculated using a simple lamellar two-phase model, which was clearly not applicable to the multiblock inverse-tapered copolymers based on the experimental results. Atomic Force Microscopy (AFM). AFM images were collected on a Veeco Multimode V, fitted with silicon cantilevers (MikroMasch) with spring constants of ca. 5 N/m, in tapping mode at a 1 μm × 1 μm scanning size, using a free oscillation amplitude near the surface (A0) = 48 nm and amplitude set point (Asp) = 32 nm (rsp = 0.67). Films were spun-cast from a 0.5% (w/v) solution in toluene onto silica wafers. Phase information was analyzed using Bruker Nanoscope software to examine cross-sectional information.

EXPERIMENTAL SECTION

Materials. Multiblock copolymers were prepared by batch living anionic polymerization in cyclohexane (99.9% purity), adapted from the method described by Leibler and co-workers.6 The discrete block (DB) and inverse-tapered block (ITB) copolymers were synthesized first by the addition of butadiene (Airgas, polymerization grade, 99.8%), followed by copolymerization of equal weights of styrene (Fischer, certified grade, 99%) and the polar modifier tetrahydrofuran (THF, Fischer, 99.9%) and n-butyllithium (Rockwood Lithium Inc., 2 wt % in cyclohexane) added in a molar ratio of THF/Li = 5. Mn values for all copolymers are 120 kg/mol, with the individual styrene and butadiene blocks as denoted in Scheme 1 for the DB copolymers. Based on the synthesis conditions, calculated Mn’s for each of the

Scheme 1. Idealized Chain-Level Representation of the Butadiene (Black) and Styrene (White) Monomer Distribution in the Discrete Block (DB) and InverseTapered Block (ITB) Copolymers Used in this Investigationa

a

In the DB-xx or ITB-xx labeling scheme, xx refers to the individual discrete or inverse-tapered block Mn values calculated from the synthesis conditions in units of kg/mol. The end blocks in the ITB copolymers are either 20K or 30K molecular weight, with the taper fractions f T designated according to the previously published convention.19 All copolymers have a total Mn = 120 000. B

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RESULTS AND DISCUSSION The multiblock copolymers used in this study are shown in Scheme 1, with discrete block copolymers and inverse-tapered block copolymers denoted as DB and ITB, respectively. In the DB-xx or ITB-xx labeling scheme, “xx” refers to the individual discrete or inverse-tapered block Mn values calculated from the synthesis conditions in units of kg/mol, an example calculation for which is presented in the Supporting Information. The end blocks in the ITB copolymers are either 20 or 30 kg/mol molecular weight, with the taper fractions f T equal to 0.67 or 0.5, respectively. The ITB-10, -20, and -30 copolymers were intentionally designed so that the tapered blocks would have average component fractions with molecular weights between the polybutadiene entanglement molecular weight Me = 2 kg/ mol and polystyrene Me = 18 kg/mol.34 Based on the copolymer Mn’s and solubility parameter data for polystyrene and polybutadiene, χN values for all copolymers used in this study significantly exceed the theoretical critical values of 10 and 29.5 for diblock and gradient copolymers, respectively.35,36 For the same end-block size, there are directly comparable DB and ITB architectures; e.g., ITB-40 is the same copolymer as DB-20, just with the discrete chain interfaces replaced with the inverse-tapered transition. ITB-60 and DB-30 are similarly related, as are ITB-20 and DB-10. Compositional details of all samples are given in the first three columns of Table 1.

shows that the ITB-10, -20, and -30 multiblock copolymers exhibit clearly resolved and relatively narrow intermediate Tg’s at 240, 236, and 231 K, respectively. For a random 50:50 styrene−butadiene copolymer whose butadiene component contains 9.5 wt % 1,2-butadiene enchainment, which is representative of the PB segments here, the predicted composition-weighted average Fox equation Tg is 247 K. In addition, the ITB-40 and ITB-60 copolymers exhibit broad averaged Tg’s ranging from 195 to 250 K, with thermograms that in no way resemble those observed for their DB-20 and DB-30 analogues. Interestingly, there is a resolved pure-PB component at ca. 190 K in the ITB-10, -20, and -30 thermograms that does not appear in the ITB-40 result. The DSC data provide limited chain-specific information in the temperature regions intermediate between the pure PB and pure PS Tg’s. For example, it is not clear to what degree, if any, that both butadiene-rich and styrene-rich chain segments contribute to the averaged Tg’s observed for the ITB-10, -20, and -30 copolymers. Variable-temperature solid-state 1H MAS NMR affords chain-specific resolution over essentially the same temperature range as the DSC data, since molecular motion associated with the onset of the glass transition eliminates homonuclear dipolar interactions between the abundant 1H spins in the copolymers leading to narrow and resolved spectral lines in the isotropic region of the spectrum. Prior to the onset of chain reorientations, the proton signal appears as a featureless, broad Gaussian signal extending over a 50 kHz region. Figure 2 shows the isotropic region of the 1H MAS spectrum as a function of temperature for the directly comparable DB-20 and ITB-40 copolymers, and for reference, the full 200 kHz spectral region containing both narrow isotropic and broad rigid lineshapes is shown in Figure S2. An obvious difference between the temperature-dependent DB-20 and ITB-40 stack plots in Figure 2 is the lack of any aromatic hydrogen signal in the DB-20, even at 340 K, while the onset of molecular motion sufficient to average homonuclear dipolar couplings leading to narrow lines begins at 240−250 K in the ITB-40 copolymer. Conversely, the butadiene signals in the DB-20 have a narrower line width at all temperatures than that observed for the ITB-40, indicating that there is a much smaller fraction of butadiene-rich chain segments that undergo temperature-dependent chain dynamics similar to that in pure PB in ITB-40. Stated simply, the ITB-40 results show that there are larger populations of butadiene-rich segments that become more conformationally restricted and styrene-rich chain segments that become more conformationally mobile, and therefore both chemical species participate in the broad intermediate Tg shown in Figure 1b for the ITB-40. A composite figure in which the chain-specific 1H MAS NMR results are superimposed with the DSC results, over the same temperature range, is shown in Figure 3 for the DB-20, ITB-20, and ITB-40 copolymers. The NMR data were taken from the PS aromatic signal at ca. 7 ppm and the PB olefinic signal at ca. 5 ppm. The MAS NMR data show, more clearly than the DSC, that the ITB-20 and -40 differ in the onset, the breadth, and the temperature-dependent slopes of individual-component Tg’s. Inverse-tapered copolymer synthesis leads to mixed monomer chain sequences,24 which should contribute to their unique Tg behavior described above. Previously, a standard-addition spin-counting method was described that quantifies the molar composition of butadiene and styrene monomer units that ultimately reside in mobile versus conformationally restricted regions in gradient copolymers.22 Briefly, a known amount of

Table 1. Compositional Heterogeneity of Styrene and Butadiene Units in Copolymer Chains as Measured from a Combination of 1H Solution NMR and 1H Solid-State MAS Spin-Counting NMR Methodsa copolymer

% Styb

% 1,4Butb

% 1,2Butb

% nonblocky Styb

DB-10 DB-20 DB-30 ITB-10 ITB-20 ITB-30 ITB-40 ITB-60

34.6 34.3 34.6 33.8 34.7 33.9 33.5 34.3

52.2 53.1 53.3 53.7 52.8 53.8 53.9 53.6

13.2 12.6 12.1 12.4 12.5 12.3 12.6 12.1

4.7 2.4 0.8 13.6 12.9 9.8 12.1 9.1

% rigid Butc

% mobile Styc

6.8

2.2

17.6 14.5

9.3 8.1

17.6

8.6

a

All copolymers were 50:50 wt:wt % or 34:66 Sty:But mol:mol %. The solution NMR calculations and designation of non-blocky styrene follow the method described in ref 37 and shown in Figures S3 and S4, while the rigid butadiene and mobile styrene in the solid state are measured according to the spin-counting method in ref 22. All units below are mol %, and data are reported for room-temperature measurements. b1H solution NMR method. c1H solid-state MAS spincounting NMR method.

Modulated DSC reversing-heat flow thermograms are shown in Figure 1 for both the mutliblock DB and ITB copolymers. The DB copolymers act as controls for interpreting the ITB behavior, and Figure 1a shows that discrete, resolved Tg’s are observed near the pure component PS and PB Tg’s for all DB’s, with the exception of the PS Tg in DB-10. DB-10 exhibits a broad, featureless transition at higher temperatures, in addition to a Tg at ca. 190 K for the polybutadiene-rich segments. As expected, increasing Tg’s for the butadiene component and decreasing Tg’s for the styrene components are observed as the discrete block size decreases from 30K to 10K in the multiblocks. However, no resolved intermediate Tg’s are observed for the multiblock DB’s. In contrast, Figure 1b C

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Figure 1. Modulated DSC thermograms for the series of multiblock (left) discrete and (right) inverse-tapered copolymers, acquired in the second heating ramp. Note that the ITB-10, -20, and -30 copolymers have clearly resolved Tg’s at 240, 236, and 231 K, respectively. For reference, the Tg’s for pure PB and pure PS are 185 and 373 K, respectively. The y-axis, in units of W K−1 g−1, is not shown for clarity, but an overlay of all thermograms on the same y-axis is provided in Figure S1 of the Supporting Information.

Figure 2. Stack plots comparing variable-temperature 1H magic-angle spinning (MAS) NMR spectra of (a) DB-20 and (b) ITB-40. The full 100 kHz spectral width was acquired, including the Gaussian rigid-lattice signal arising from primarily polystyrene. For convenience and resolution of line shapes in the mobile phase, each spectrum is presented in an expanded view of the narrow isotropic region of the total spectrum from 190 to 340 K. Representative spectra showing the full spectral region are shown in Figure S2, and variable-temperature plots for all copolymers are shown in Figures S6 and S7.

Figure 3. Combined representation of a subset of the DSC (left axis) and the variable-temperature MAS NMR data (right axis) comparing the temperature-dependent behavior of (a) DB-20, (b) ITB-20, and (c) ITB-40 copolymers. The chain-specific information afforded by the individual peaks in the MAS NMR experiment reveals a significant decrease in the Tg for the styrene components in the ITB chains, with a ca. 10-fold increase in its Tg range relative to styrene in the DB analogue in the ITB-40 case. Similarly, the ITB butadiene segments show an increase in both magnitude and breadth of their Tg’s. The NMR data and y-axis are plotted as percent of total signal appearing in the mobile phase, i.e., the isotropic region of the spectra, as shown in Figure 2.

determine the intensity per 1H in the spectra. This provides a quantitative means to compare observed signal intensities to expected values based on measured sample mass and known chemical composition. The full 200 kHz spectral width is used in order to accurately assign narrow signals to mobile chain

polydimethylsiloxane (ca. 5% of the total mass) is added to a known amount of copolymer sample in a centrally confined region of the MAS rotor to minimize radio-frequency field inhomogeneity. Comparison of the total integrated intensity of the PDMS signal with measured PDMS mass allows one to D

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Figure 4. Selected solution 1H NMR spectra comparing DB-20 to three ITB copolymers, as indicated by color. In the absence of color, the spectra are arranged top to bottom in the same order as the legend. The dashed boxes highlight selected signals arising from mixed comonomer sequences in the ITB copolymers that do not appear in any of the discrete block spectra. Calculation of butadiene monomers alpha to styrene monomers, and vice versa, as well as the overall amount of non-blocky styrene37 are illustrated in Figures S3 and S4 and Table S1 based on the aromatic and olefinic signal regions in the dashed boxes.

Figure 5. Selected solution 13C NMR spectra comparing the aromatic and olefinic spectral region of the representative DB-20 versus three ITB copolymers, as indicated by color. In the absence of color, the spectra are arranged top to bottom in the same order as the legend. The dashed boxes highlight selected signals arising from unique comonomer sequence effects in the ITB copolymers that do not appear in any of the discrete block spectra but are consistent with previously assigned signals in random copolymers.38,39 Detailed spectra, HSQC data, and assignments with chemical shift tables are given in Table S2 of the Supporting Information and associated figures.

Figures 4 and 5 show representative 1H and 13C solution NMR spectra for the same DB and ITB copolymers analyzed by the solid-state spin-counting method, with mixed-monomer diad and triad sequences labeled according to previously published assignments in styrene−butadiene random copolymers.37−39 Previously, Sardelis and co-workers have used the term “nonblocky styrene” for sequence-shifted signals of ortho-hydrogens in styrene units alpha to butadiene in the comonomer chain,37 and Figures S3 and S4 detail how calculations with this 6.2−6.7 ppm 1H signal are used to determine the values in Table 1 for the column labeled “% non-blocky styrene”. Note the expected increase in this component for DB-10 over DB-20, both of which exceed that in DB-30. Similar to the 4-fold increase in the % mobile styrene from the solid-state spin-counting experiment, there is on average a 5-fold increase in the amount of nonblocky styrene in the ITB’s relative to the DB-20 copolymer. Spin-diffusion methods can, in a noninvasive experiment, reveal the average minimum domain sizes in amorphous polymer blends and copolymers. Dipolar-filter 1H-detected spin-diffusion NMR experiments30,31 were used to probe

segments versus broad Gaussian signals to rigid chain segments. Chemical shift resolution allows component specific determination of rigid butadiene and mobile styrene amounts, the components indicative of a third “interphase” morphological region in the solid copolymers, using isotropic signal areas. On the basis of the results in Figures 1−3, one should expect significantly different amounts of these components in the ITB compared to the DB copolymers. Obviously, pure polybutadiene has only mobile segments, and pure polystyrene has only rigid segments. Results of the spin-counting experiment are reported in the last column of Table 1 for the DB-20 and the ITB-10, -20, and -40 copolymers. The results show that the mole percent of rigid butadiene chain segments increases by a factor of 2.5, while that for mobile styrene units increases by a factor of 4, in the ITB’s relative to the DB-20 control polymer. Again, these measurements are made on the solid copolymers from the polymerization reactor, without any additional thermal treatments or solvent exposure. The amount of mobile styrene in the solid state should be related to the polymer microstructure, which is best probed through a combination of solution NMR methods. E

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Macromolecules average minimum domain sizes for the DB and ITB copolymers. The total polarization is modified such that only the most mobile (long-T2) spins serve as the initial polarization source, which gets redistributed to all spins during a mixing time and whose characteristic rate is reflective of the size of that mobile domain source. As previously demonstrated by Molnar and co-workers, estimates of interfacial thicknesses can be made with this approach through varying the strength of the dipolar filter used and thus the initially selected polarization source within the copolymer.31 Here, three looped cycles of the basic dipolar filter sequence with an interpulse spacing of 10 μs were used to prepare the polarization gradient and select the polybutadiene-rich phase as the source. Figure 6 shows the

contributions to the decay. The DB-10 and -20 samples serve as controls, since their known lamellar morphology allows calculation of their domain sizes using standard practices32 involving identification of the characteristic spin-diffusion equilibration time τm0.5, as illustrated in more detail in Figure S8. Note the break in the y-axis in Figure 6; a full axis is shown in Figure S8. Using the standard diffusion equation, domain sizes for the polybutadiene source phase in the experiment are calculated as 9.3 and 12.6 nm for the DB-10 and DB-20, respectively, using an effective diffusion coefficient of Deff = 0.249 nm2/ms that was determined based on the T2 of the mobile phase and the known diffusion coefficient of rigid PS (Dmobile = 0.0209 and Drigid = 0.8 nm2/ms, respectively).32,33 The domain size for DB-10 is less than DB-20, and DB-30, which is not shown in Figure 6, had an even larger polybutadiene domain size of 14 nm, all as expected. These values are in agreement with previously published AFM data23 and with the 12.3 ± 1.7 nm domain sizes extracted from linear cross sections in the AFM image of DB-20 in Figure 7b. These intermediate nanoscopic dimensions are consistent with the fact that equivalent 1H T1 values of ca. 0.5 s are observed for all main-chain PB and PS signals for all copolymers, but their T1ρH relaxation time constants do not converge to a common value for PB and PS signals, as would be expected for microphase separation. Finally, the equilibrium polarization “plateau” at long spin-diffusion times for the DB control polymers of 0.62 is in agreement with the compositional data in Table 1, in which the mole fraction of polybutadiene spin-diffusion source in DB10, -20, and -30 is 0.65. That the 0.65 value is slightly reduced to 0.62 is consistent with the larger value of rigid butadiene versus mobile styrene from the small interfacial volume of the DB-20, as shown in the last two columns of the second line in Table 1. The shaded region denotes the expected range for the plateau source value for a discrete block copolymer, with the upper limit of 0.65 defined by the copolymer composition and the assumption that no interphase exists. The lower value of 0.57 is defined by the most stringent dipolar filter sequence that preserves measurable signal. Note that none of the ITB copolymers reach an equilibrium plateau value within the shaded region. The slight increase in the spin-diffusion curves at long spin-diffusion times arises from imperfections at canceling T1 effects at long mixing times. The control experiments on the DB systems allow confidence interpreting the raw spin-diffusion data for the

Figure 6. Static spin-diffusion curves for the indicated copolymers, obtained with a direct-observation 1H dipolar filter experiment30 and T1 compensation via parallel/antiparallel storage pulses. Note the break in the y-axis. Three cycles of the 12-pulse π/2 filter with a 10 μs interpulse spacing were used, resulting in a polarization gradient that selected only mobile source spins. The mobile source fraction evident at long times increases with introduction of inverse-tapered sequences, as does the curve complexity in the short time region, indicating the presence of significant interphase volume. For comparison, Figure S7 shows the initial rate extrapolation with full y-axis used for the DB-10 and DB-20 domain size calculations. The shaded region is explained in the text.

results of these experiments on the DB and ITB copolymers acquired under static conditions, in which the intensity loss of the source signals to the more rigid regions of the copolymers is plotted versus time. All points are corrected for 1H T1

Figure 7. Tapping-mode AFM phase contrast images of (a) a discrete diblock copolymer with Sty-But blocks of Mn = 25K, (b) DB-20, and (c) ITB20 copolymer films. The dark regions correspond to soft butadiene-rich phases, while the light regions are the more rigid styrene-rich phases. Note the loss of phase contrast in ITB-20. Examination of multiple linear cross-section yield domain sizes of 30 ± 9 nm for (a) and 12.3 ± 1.7 nm in (b). Lack of sufficient phase constrast and an apparent cocontinuous morphology in (c) precluded identification of minimum domain sizes. F

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rich regions reveals behavior that is unique to each ITB design, even though the total amount of butadiene and styrene in the interphase region, as measured by the sum of rigid butadiene and mobile styrene, is relatively constant across the ITB designs. In total, the experimental results suggest that multiblock ITB copolymers can be tailored to address a potentially wide range of polymer properties, particularly when choosing components with large differences in the Tg’s of their respective homopolymers.

ITB-10, -20, and -40. The standard initial-rate model, demonstrated in Figure S8 and described above for typical domain size calculations involving only two components, does not fit the three curves for the ITB copolymers, as expected from their complex decay shown in Figure 6. In addition, examination of the spectra following the dipolar filter selection, but prior to any spin-diffusion mixing time, shows significant signal intensity from PS spins in the mobile “source” phase (not shown) for all ITB’s, indicating that a butadiene-only specific polarization gradient cannot be created in the ITB as occurs in the DB copolymers. Finally, the increased plateau values at long spin-diffusion times indicate large interphase compositions of mixed styrene−butadiene segments that are not observed in the DB copolymers, as expected from the solution NMR data described above and consistent with the AFM data in Figures 7a−c. Specifically, Figure 7c shows a highly mixed and essentially cocontinuous phase for the ITB-20 copolymer with little phase contrast between butadiene- and styrene-rich domains. Note that the short, medium, and long-time spindiffusion behavior differs among the three ITB copolymers. In order to fully characterize interphase dimensions and volume fractions using only spin-diffusion, comparisons of experiments in which the mobile chains are the source versus those in which the rigid chains serve as the source would be necessary40 as well as analytical solutions to the spin-diffusion curves. However, the noninvasive and nonperturbative spin-diffusion experiments shown in Figure 6, which do not require the inherent solventannealing step common to AFM data or thermal cycling inherent to DSC, unequivocally demonstrate a significant interphase in the solid ITB copolymers. The data in Figure 6 were acquired directly on the polymers obtained from the reactor, with no subsequent thermal or solvent treatment. The data discussed above, including the rigid butadiene and mobile styrene fractions from spin-counting data for the f T = 0.5 copolymers listed in the last two columns of Table 1, as well as the comparison of data in Table S1 for f T = 0.5 and 0.67 cases, clearly suggest that the taper fraction is a defining characteristic in controlling Tg’s and chain-segment dynamics in tapered copolymers. That our experimental results provide this conclusion is in agreement with recent theory papers in the literature.20,41

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b01476. One- and two-dimensional solution NMR data detailing composition and microstructure, the complete range of variable-temperature MAS NMR data showing temperature-dependent chain dynamics in the solid state, and sample calculations (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail jeff[email protected] (J.L.W.). *E-mail [email protected] (J.Z.). ORCID

Jeffery L. White: 0000-0003-4065-321X Present Address

J.Z.: Chevron Phillips Chemical Company LP. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the National Science Foundation (GOALI grant DMR-1606364) and Chevron Phillips Chemical Company LP for support of this work. The authors thank the Oklahoma State University Microscopy Laboratory, which received funds for purchasing equipment from the NSF MRI program, for AFM access.

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CONCLUSIONS Detailed calorimetry and solid-state NMR experiments have shown that multiblock inverse-tapered copolymers with overall Mn equal to 120 000 can exhibit a wide range of Tg’s and individual chain dynamics based on the size and number of inverse-tapered blocks. In some cases, composition-weighted average glass transitions near the 247 K value expected from the Fox equation are observed and which cannot be duplicated using discrete multiblock copolymers with similar block number, block size, and overall Mn. A range of intermediate glass transitions was observed, but the inverse-tapered copolymers with individual block molecular weights between the entanglement molecular weight (Me) of PS and PB were the only copolymers that exhibited a Tg near the predicted composition-weighted average. Solid state NMR experiments reveal that the amount of styrene units that get incorporated into low-Tg mobile regions quadruples for the ITB’s compared to their DB analogues. Similarly, the number of butadiene units incorporated into rigid, high-Tg regions increases by a factor of 3 in the ITB’s. Chain-level measurement of temperaturedependent chain dynamics for the styrene-rich and butadiene-

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DOI: 10.1021/acs.macromol.7b01476 Macromolecules XXXX, XXX, XXX−XXX