Thermodynamics of Chain Architecture in Acrylic Block Terpolymers

Article pubs.acs.org/Macromolecules

Thermodynamics of Chain Architecture in Acrylic Block Terpolymers James A. Bergman, Nacú B. Hernández, Eric W. Cochran,* and Jennifer M. Heinen Department of Chemical and Biological Engineering, Iowa State University, Ames, Iowa 50011, United States S Supporting Information *

ABSTRACT: In this article, we report the manipulation of block terpolymer morphology through control of the segment distribution. We consider a model system comprised of three acrylic monomers: hydrophilic poly(hydroxyethyl acrylate) (H), hydrophobic poly(octyl acrylate) (O), and polar poly(methyl acrylate) (M). For each of four chemical compositions, we altered the M segment distribution in four terpolymer architectures with reversible addition−fragmentation chain transfer (RAFT) polymerization to yield: two triblock terpolymer architectures, HOM and HMO, and two diblock terpolymer architectures, HM/O and H/MO, where the M segments are statistically distributed in the O or H blocks, respectively. Using a combination of small-angle X-ray scattering and dynamic shear rheology, we illustrate how the monomer distribution can be used to manipulate the thermodynamic behavior of terpolymers at constant chemical composition. These results will be of use to those wishing to partially decouple the formulation of a block copolymer from its morphology.

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INTRODUCTION The self-assembly of block copolymers (BCPs) has received much attention over the past 40 years and the thermodynamic behavior of diblock copolymers is well understood.1−5 Diblock copolymers are known to self-assemble into a limited number of microstructures: body-centered cubic packed spheres (Q229), hexagonally packed cylinders (H), orthorhombic Fddd network (O70), double gyroid (Q230), and lamellae (L). Manipulating BCP self-assembly may be achieved by changing the composition (fA), chemistry (Flory interaction parameter χAB and Kuhn lengths bi), and segregation strength (∝N/T, where N is the degree of polymerization and T is the absolute temperature). In a qualitative sense, the phase behavior of diblock copolymers is universal; that is, the sequencing of phases with composition and temperature is fixed and only the quantitative locations of the phase boundaries vary from system to system. In principle, the simplicity of this universal phase behavior is desirable from an applications design perspective. In practice, however, the design of an application fixes the chemistry and places constraints on the composition and segregation strength. This facet of the copolymer parameter space unfortunately means that the simultaneous optimization of chemical composition and retention of the desired morphology may be unachievable. That is, simplicity comes at the expense of flexibility. Alternatively, the phase space of triblock terpolymers is known to be far more expansive due to the number of independent variables that describe the system; the parameter space now includes an additional two interaction parameters (χBC and χAC) and an additional independent volume fraction (f B).6 The addition of the third C component increases the © XXXX American Chemical Society

number of possible microstructures by at least 5-fold, to date over 30 microstructures have been identified.7 Numerous groups have contributed to our collective understanding of how multicomponent block copolymers behave with the introduction of additional interfaces. Much of the first work in this was produced by the research groups of Stadler,8−11 Abetz,12−14 and Matsushita; 15−17 many reports included countless juxtapositions of diblock copolymer-like structures. For example, a number of “decorated” phases such as spheres-onspheres,18 a tetragonal lattice of A and C cylinders in a B matrix,17 tetragonally perforated lamellae,19 or A and C spheres in a CsCl-like packing.17 Moreover, fascinating new structures such as the “knitting pattern”20 and the orthorhombic network phases O70 and O52 were quite unlike any structure observed in soft matter21,22 (although O70 was later discovered in diblock copolymers3,5). Star architectures, various blending strategies, and even the introduction of a fourth component have further supplemented the current palette of known mesophases. While the possibilities attendant with the ever-increasing complexity and richness of polymer phase behavior continue to captivate researchers’ imaginations, complexity is not necessarily ideal for material design. This article presents work in which we begin to explore the role of the C component as a tool that can be used to simplif y the task of block terpolymer design while retaining the f lexibility engendered by the third component. That is, given a fixed chemical composition, we seek to establish the design Received: May 1, 2014 Revised: August 1, 2014

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dx.doi.org/10.1021/ma500905n | Macromolecules XXXX, XXX, XXX−XXX

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domains can be used to synthesize A/B/C “triblock−random” terpolymers with tunable segregation strengths between each random block.40 As with the tapered A/B/C distributions the resultant permutations of possible products becomes quite large. In this work, we employ a model system comprised of three types of acrylic segments: poly(hydroxyethyl acrylate) (H), a hydrophilic polymer; poly(methyl acrylate) (M), a polar polymer; and poly(octyl acrylate) (O), a hydrophobic polymer. As we will show, the interaction parameters for this system satisfy the sequence χHO ≈ 2χHM ≈ 2χMO. The H/O system is of technological interest as a source of a new family of amphiphilic materials; the simplest such material would be the diblock copolymer HO whose phase behavior is governed by f H and χHON. We show that the introduction of M, with intermediate polarity, serves to influence the phase morphology and transition temperatures while leaving the chemical composition and molar mass fixed. The terpolymer architectures depicted in Figure 1 illustrate a thought experiment in which M (block “B”) segments progress from “right” to “left” in chain architectures a−d. Figure 2 plots the copolymer

rules associated with the segment distribution function in a model A/B/C “three-color” system. This work is conceptually related to the “gradient”23−28 or “taper”29−33 architectures in A/B copolymer systems. As Figure 1 illustrates, the monomer

Figure 1. Schemes for manipulating block polymer self-assembly through the segment distribution. (Left) The segment distibution of diblock copolymers can be manipulated in many ways, for example by using a combination of sequential and gradient copolymerization techniques. In this way the transition from A to B occurs gradually along the chain contour. Tuning this transition allows the decoupling of χeff from design parameters f and N (Right). In ternary systems, manipulation of the sequence distribution can influence both the effective domain composition f * and the effective interaction strength χeff, partially decoupling both the chemical composition and molecular weight from the thermodynamically preferred morphology.

sequences embodied by these two copolymer types lie on one of many paths that span the continuum between a purely statistical A/B copolymer and a perfectly discrete AB diblock copolymer. Gradients and tapers are typically prepared using a semibatch reaction scheme in conjunction with a (pseudo)living polymerization chemistry, e.g., nitroxide-mediated radical polymerization,25 atom transfer radical polymerization,23 reversible addition−fragmentation chain transfer (RAFT) polymerization,28 or anionic polymerization.29,30 In essence, the width of the chemical A/B interface maps to the width of the corresponding spatial interfaces, and accordingly the effective segregation strength of the copolymer χeffN can be tuned through simple reaction engineering, leaving the overall molecular weight and chemical composition fixed. The extension of this principle to three-color systems is straightforward; again semibatch addition techniques may be used to taper the A/B/C segment distribution,34 although the number of resultant permutations of polymers that can be produced becomes large. Moreover, the “trivial” case in the engineering of diblock copolymers through sequence distributionthat is, the statistical A/B copolymeris no longer trivial in the analogous progression of possible A/B/C sequence distributions. Rather, sequences such as AB/C or A/BC represent intermediates in the progression from BAC to ABC to ACB. Statistical A/B copolymer domains can be incorporated into block copolymer architectures to form “block−random” AA/B copolymers. Similar to the taper and gradient architectures mentioned above, block−random architectures can be used to manipulate the effective segregation strength of the copolymer. Studies by Beckingham et al. and Roasles et al. have shown AA/ B copolymers can tune TODT independent of block volume fraction and molecular weight.35−37 Only recently have systematic studies extended the “block−random” copolymers to the terpolymer AB/C regime,38,39 where the statistical B/C copolymer domain can be used to incorporate a new monomer chemistry and thus new properties. Additionally, statistical A/B

Figure 2. Composition diagram for H/M/O system investigated in this study. Details for compositions 1−4 are listed in Table 1

compositions that were synthesized for this work on the H/ M/O ternary composition diagram. We hypothesized that for the H/M/O systemat sufficiently small M volume fraction f Mthe phase behavior of all architectures should mimic that of classical diblock copolymers. That is, for the purposes of targeting a particular morphology, it should be possible to define a mapping of the three χ parameters and two composition variables to a reduced “diblock-equivalent” parameter space that defines an effective domain composition f * and interaction strength χeff that serve as a first-order predictor for the thermodynamic behavior of a particular material. For diblock terpolymers, i.e., H/MO and HM/O, there is clearly a single interface that partitions the polymers into twodomain morphologies that implies diblock-copolymer-like phase behavior. On the other hand, the triblock architectures HMO and HOM will be governed by competing H/M and O/ M interfaces where no such simplifying mappings can necessarily be prescribed.

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EXPERIMENTAL SECTION

Chemicals. Anhydrous ethanol (200 proof), carbon disulfide (99%), hydroxyethyl acrylate (96%), and ethyl α-bromoisobutryate (98%) were purchased from Sigma-Aldrich Chemical Co. and used as B


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Table 1. Molecular Characteristics of the 19 copolymers Considered in This Papera

Three diblock copolymers were evaluated to quantify the χ-parameters of the H/M/O system. A total of 16 terpolymers were produced to illustrate the utility of the segment distribution to manipulate the morphology: each terpolymer represents one of four distinct chemical compositions and one of four segment distribution functions. a

received. Potassium hydroxide (85%), tetrahydrofuran (THF), and 1,4-dioxane were purchased from Fisher Scientific and used as received. Methyl acrylate (99%) and n-octyl acrylate (96%) were purchased from Sigma-Aldrich and Scientific Polymer Products respectively; both were passed through an SDHR-4 column, purchased from Scientific Polymer Products, to remove the inhibitors hydroquinone and monomethyl ether hydroquinone prior to use. The initiator 2,2′-azobis(isobutyronitrile) (98%) was purchased from Sigma-Aldrich and was recrystallized in ethanol prior to use. Reversible Addition−Fragmentation Chain Transfer Agent Synthesis. The reversible addition−fragmentation chain transfer agent (RAFT CTA), ethyl 2-(ethoxycarbonothioylthio)-2-methylpropanoate (ETMP) was synthesized using a procedure adapted from Stenzel et al.41 Potassium hydroxide (0.05 mol) was stirred in ethanol (20 mL) at room temperature until it completely dissolved. Then carbon disulfide (10 mL) was added over 90 min, and the solution was allowed to stir for 5 h. Ethyl α-bromoisobutyrate (14.8 mL) was added and the solution was stirred for 12 h before the mixture was filtered and the ethanol was removed by evaporation. The resulting yellow liquid was diluted with diethyl ether and twice passed through a chromatography column packed with basic aluminum oxide. The diethyl ether was evaporated and 1H NMR was used to verify the structure of the product. The 1H NMR spectra were collected on a Varian VXR-300 spectrometer using CDCl3 as solvent at room temperature. 1H NMR (300 MHz, CDCl3): δ 1.27 (t, 3H, CH3CH2), δ1.39 (t, 3H, CH3CH2), δ1.61 (s, 6H, CCH3), δ4.17 (m, 2H, CH3CH2), δ4.59 (m, 2H, CH3CH2). Terpolymer Polymerizations. Diblock and triblock terpolymers of hydroxyethyl acrylate (H), methyl acrylate (M), and octyl acrylate (O), were prepared by RAFT polymerization with sequential monomer addition using ETMP as the CTA. The molecular

characteristics of the 19 polymers synthesized are tabulated in Table 1. The volume fractions reported in Table 1 were calculated using the monomer densities at 25 °C as reported by the supplying companies: H, 1.011 g/mL; M, 0.956 g/mL; O, 0.876 g/mL. Homopolymer melt densities were assumed to be proportional to the monomer densities. We found that in these polymerizations, H showed poor initiation effiency from O or M macro-CTA moieties. For this reason, H must be polymerized first, either as a homopolymer block or as a copolymer block with M. Kinetic studies for hompolymerizations of each monomer indicated that complete monomer conversion was attained at: 75 min for H, 90 min for M, and 120 min for O. Kinetic data of monomer conversion (ln[M]/[M]0) versus time (min) for the homopolymerizations of each monomer are shown in Figure 3. Least squares regression of the conversion data to a first-order kinetic model yields apparent rate constants for each monomer: kH = 0.063 min−1, kM = 0.033 min−1, and kO = 0.021 min−1. The synthesis of an exemplar triblock terpolymer polymerization of HMO-2, is as follows. H (5.44 mL, 5.50 g, 46 mmol) and the chain transfer agent ETMP (0.21 g, 0.84 mmol) were dissolved in 20 mL of dioxane in a round-bottom flask with a magnetic stir bar. The initiator 2,2′-azobis(isobutyronitrile) (AIBN, 0.013 g, 0.084 mmol) was added at a 1:10 molar ratio relative to ETMP. The round-bottom flask was sealed with a rubber septum, and the solution was purged with argon for 10 min at 25 °C prior to heating to 65 °C. The polymerization was allowed to proceed for 2.5 h, then an aliquot was removed for subsequent measurements of conversion and molecular weight. This monomer:CTA ratio was chosen to produce an H block with 54 H repeat units and Mn,H = 6.5 kDa at 98% conversion. M (1.53 mL, 1.45 g, 17 mmol) was purged with argon, and introduced to the roundbottom flask via syringe pump. This monomer:CTA ratio was chosen to produce an M block with 20 M repeat units and Mn,HM = 8.2 kDa at C


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Figure 4. SEC chromatographs for composition 3 of each architecture. Figure 3. Homopolymer conversion versus time for O (filled squares), H (filled triangles), and M (open circles) polymerization.

Samples were then examined (under contract) by Dr. Claire Pizzey of the Diamond Light Source, Ltd., in Didcot, Oxfordshire, OX11 0DE, U.K., at beamline I22. SAXS data for the samples were collected at ambient temperature using 12.4 keV xrays and a Pilatus 2 M area detector. The momentum transfer (q) calibration was performed using a silver behenate standard, which was also used to determine the beam center position. 120 frames of one second exposure each were acquired per sample, to allow for subsequent data evaluation to assess radiation damage. Data reduction was performed in a standard manner using software developed at Diamond. Advanced Photon Source. SAXS experiments were conducted at beamline 12-BM-B at the Advanced Photon Source, Argonne National Laboratory. Tzero differential scanning calorimeter (DSC) low-mass pans and hermetic lids (part numbers 901670.901 and 901684.901 respectively) were purchased from TA Instruments of New Castle, DE. A small amount of the material of interest was put into a DSC pan and lid and sealed using a TA Instruments Tzero pan press. SAXS data for the samples were collected at various temperatures ranging from ambient to 250 °C on beamline 12-BM-B at the Advanced Photon Source using 11.0 keV X-rays and a MarCCD165 (Rayonix, LLC) detector over a q range of 0.007 to 0.44 Å−1. A Linkam THMS600 heating and freezing stage (Linkam Scientific Instruments Ltd.) was used to control sample temperature. The momentum transfer (q) calibration was performed using a silver behenate standard, which was also used to determine the beam center position. Data were acquired with single, continuous exposures with exposure times ranging from 5 to 20 s. Data reduction was performed in a standard manner using Fit2D software developed by Dr. Andy Hammersley.43 All data were normalized to the transmitted beam intensity. Data were plotted in excel. The primary scattering and reflection scattering peaks were identified using software developed by Dr. Eric Cochran. Rheology. Flory−Huggins interaction parameters (χ) for HO, HM, and MO diblock polymers were determined rheologically (Table 2). A Rheometrics ARES-LS1 strain controlled rheometer with a

98% conversion. After 3 h a small aliquot was removed, and argonpurged O (3.13 mL, 2.74 g, 15 mmol) was fed to the round-bottom flask via syringe pump slowly, at a rate of 0.021 mL/min, to prevent phase separation of the H. The O was allowed to react for 2 h after the feeding was complete. This monomer:CTA ratio was chosen to produce an O block with 17 O repeat units and an Mn,HMO = 11.3 kDa at 98% conversion. Complete monomer conversion for each block was verified gravimetrically, and polymer molecular weight was determined by size exclusion chromatography (SEC). Copolymerized blocks were synthesized via a semibatch method with an initial charge of M followed by a slow addition of H or O. The H and O feeds were controlled via syringe pump equipped with gastight syringe. The feed rates were manipulated such that H was fed over 1 h and O was fed over 2 h. These feed rates were chosen empirically such that the consumption rate of both M and the comonomer were appropriately proportional throughout the polymerization as evidenced by 1H NMR. Size Exclusion Chromatography. Polymer molecular weight and polydispersity were determined by size exclusion chromatography (SEC). The instrumentation consisted of a Waters in-line degasser AF, a Waters 515 HPLC pump, a Waters 717Plus autosampler, a DAWN HELEOS II MALLS detector, and an Optilab T-rEX RI detector set at 658 nm wavelength. Samples were made by dissolving 10−15 mg of polymer in 1 mL of HPLC-grade tetrahydrofuran (THF), and then filtering the solutions using low protein binding Durapore 0.22 μm filters. Samples were passed through four PLgel 5 μm, 7.5 mm ID SEC columns purchased from Varian Inc., in the following order: 50 mm guard column, 300 mm 100 Å column, 300 mm 500 Å column, and 300 mm 10 000 Å column. THF was used as the eluent at a flow rate of 1 mL/min. Data were collected and analyzed using Astra 5.3.4 software by Wyatt Technology. The derivative of refractive index with respect to composition was approximated as dn/dc = 0.082 mL/g for all polymers; this value was reported for a polymer of poly(methyl methacrylate/butyl methacrylate) (60/40 mol) at 63 kDa and was chosen for the purpose of determining polydispersity.42 Representative SEC traces for composition 3 appear in Figure 4. Small Angle X-ray Scattering (SAXS). Diamond Light Source. Standard differential scanning calorimeter (DSC) aluminum pans and lids (part numbers 900786.901 and 900779.901 respectively) were purchased from TA Instruments of New Castle, DE. Muscovite mica of V-1 quality, in 50 mm by 75 mm sheets that were 0.15−0.21 mm thick (part number 71855−01) were purchased from Electron Microscope Sciences of Hatfield, PA. Centered, 3 mm holes were punched into the DSC pans and lids and 5 mm disks were punched out of the mica sheets. A small amount of the material of interest was sandwiched between two mica discs. The mica−sample−mica was then put into a DSC pan and lid. The DSC pan and lid were sealed using a TA Instruments Tzero pan press.

Table 2. Summary of Diblock Copolymers Used for a First Approximation of Flory−Huggins Interaction Parameters (χ) between Each Monomer Pair (HO, HM, and MO).a

Here χ is estimated at room temperature (293 K) using eq 1 and degrees of polymerization (N) is determined with a reference volume of 149 Å3 per molecule. a

D


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convection oven was used under nitrogen gas flow to prevent polymer degradation. The HM polymer was pressed into 25 mm diameter discs with 1 mm thickness with a Carver press at 80 °C prior to being tested. The HO and MO polymers were measured without pressing due to their low glass transition temperature. The polymer samples were subjected to a 10 °C per minute temperature ramp at a constant strain of 3% and with a frequency of 1.0 radians per second. A plot of the dynamic elastic modulus (G′(Pa)) versus temperature (°C) was produced and is shown in Figure 5. This plot was then used to

RESULTS Interaction Parameters for the H/M/O System. Order− disorder transition (ODT) characterization of the diblock copolymers HO, HM, and MO were assessed with isochronal temperature scans of the dynamic shear modulus as shown in Figure 5. The ODT temperature, TODT, can be identified as the temperature at which the slope of the dynamic modulus drastically decreases. The identified TODTs are listed in Table 2, and were used in the calculation of χ for H/O, H/M, and M/O. As the polymers are symmetric (i.e., all block volume fractions are approximately equal to 0.5), the accepted χN for estimating χ at the ODT is 10.5.44 From these experiments, we see the interaction between H and M is very similar in magnitude as the interaction between O and M. Additionally, the interaction between H and O is approximately twice as large as the interaction between M and either monomer, i.e. χHO ≈ 2χHM ≈ 2χMO. The calculated interaction parameters are presented in Table 2. Terpolymer Synthetic Details. The four terpolymer architectures (a−d) were synthesized at four compositions (1−4) as enumerated in Table 1 and illustrated in Figure 2. Volume fractions reported in Table 1 were calculated using the monomer densities at 25 °C. No single source has reported homopolymer melt density for all species at a single temperature; the polymer melt densities were assumed to be proportional to the monomer densities at room temperature. All 16 terpolymers were designed such that the total molecular volume was ≈11 800 mL/mol, thus keeping N the same for all polymers. The diblock architectures, HM/O and H/MO, have compositions that span a wide range of block volume fractions. The block development and polymer growth was followed by gravimetric conversion and SEC; representative SEC results for the four architectures at composition 3 are shown in Figure 4. The molecular weight (Mn) data as determined by SEC indicate that the polymers possess Mn ranging from 11 to 24 kDa. The main reason for variations in the molecular weight is incomplete activation of the RAFT chain transfer agent; as a lower percentage of the RAFT agent is activated the molecular weight is expected to increase proportionally. This proportional increase is expected for each monomer block, therefore the polymers with high molecular weights still possess the volume fraction compositions reflected in Table 1. Additionally, incomplete CTA activation implies that di- and triblock

Figure 5. Isochronal temperature sweep of the dynamic modulus at ω = 1.0 rad s−1 for each diblock copolymer. ODT onset temperatures were used for the approximation of χ.

estimate the onset temperature of the order to disorder transition (TODT), and interaction parameters were estimated at 20 °C using eq 1, neglecting any excess entropic contribution to χ, and a methyl acrylate reference volume of 149 Å3.

χ293K = 10.5

TODT N (293 K)

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(1)

Master curves for the investigated terpolymers were produced on the same Rheometrics ARES_LS1 strain controlled rheometer. The terpolymers were measured under air, with isothermal frequency sweeps ranging from 0.1 to 100 radians per second using a maximal strain amplitude of γmax = 12. Frequency sweeps were taken every 20 °C from 35 to 175 °C, and shifted according to the time−temperature superposition principle to construct master curves; all master curves use a reference temperature of Tref = 55 °C.

Figure 6. Reaction studies of the H/M (triangles) and O/M (squares) copolymerizations. (a) Gravimetric monomer conversion with respect to time (hours). Dashed lines indicate the linear conversion rates in the nondiffusion limited regime. (b) Growth of molecular weight (Mn) versus gravimetric conversion. The dashed lines highlight the near linear growth of Mn observed as conversion increases. (c) Mole fraction of M (xM) as determined by 1H NMR at different gravimetric conversions. The expected xM for each system is represented by a horizontal dashed line. The plot shows consistent compositions of M, independent of conversion, for the copolymers. E


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Figure 7. SAXS for all materials at room temperature. The azimuthally integrated scattering intensities for each of the four polymers of a specific composition are shown in each window: upper-left (1), upper-right (2), bottom-left (3), and bottom-right (4). Primary scattering peaks and reflections are indicated with black arrows and numbers that correspond to q/q* ratios. Locations of q* and domain spacings (d) are reported in Table 1

versus time in Figure 3. From this we see that kH = 0.063 min−1, kM = 0.033 min−1, and kO = 0.021 min−1. Homopolymerization rate constants on the same order of magnitude indicate that statistical copolymers can be produced from semibatch copolymerization, irrespective of the reactivity ratios. Copolymerization kinetic studies presented in Figure 6 illustrate both that the xanthate CTA (ETMP) promotes (pseudo)living RAFT polymerization and that the semibatch copolymerizations yield statistical copolymers. Figure 6a shows the gravimetric monomer conversion as a function of time. In both the H/M and O/M copolymerizations, the conversion tracks linearly with time up to high conversions (80% or more). At high conversions, diffusion rates limit the reaction rates slowing monomer conversion. Linear dashed lines have been added to Figure 6a to highlight the linearity of the nondiffusion limited regime. The linear consumption of monomer with time indicates these copolymerizations follow the pseudo-first order mechanisms observed in the homopolymerizations. To establish the controlled (pseudo)living character of ETMPmediated RAFT polymerizations, Figure 6b plots the molecular weight versus conversion. In both the H/M and O/M copolymerizations the molecular weight (Mn) grows linearly with gravimetric conversion, a defining characteristic of (pseudo)living polymerizations.49 Moreover, the final molecular weights of the copolymers are closely predicted by the monomer to CTA ratios using eq 2:

copolymers will have contamination with their homo- and diblock copolymer percursors, which is evident in Figure 4 through the low-molecular weight shoulders. Peak deconvolutions using superpositions of Schulz−Zimm distributions indicate that these homo- and diblock copolymer contaminants account for less than 5% of the mass of the final product; thus, while in the strictest sense these materials are “blends,” ample evidence in the literature shows that we can expect our samples to behave as pure block copolymers with compositions equal to the overall composition of the “blends”.45−47 The effectiveness of the RAFT system used to produce the terpolymer architectures is illustrated in the realization of low polydispersity indices (PDIs, tabulated in Table 1). With the exception of outliers HOM-2 and HM/O‑1, PDIs fall within the range [1.09, 1.24]. In contrast to reports that xanthatemediated RAFT is problematic for acrylic monomers,48 we have found that our choice of CTA shows excellent (pseudo)living character as evidenced by the low polydispersities reported in Table 1 and in the kinetic data we present below. The high PDIs in HOM-2 and HM/O‑1 are due to the partial phase separation which occurs upon the addition of O or O /M monomer to mixtures containing H homopolymers. This was more pronounced in HOM-2 and HM/O‑1 due to their comparatively large H blocks. Kinetics for the homopolymerization of each monomer were studied to ensure that statistical copolymers could easily be produced. As the data in Figure 3 indicate, the monomer consumption rate is consistent with the pseudo-first order expression −d[M]/dt = kapp[M]. Apparent rate constants for homopolymerizations are shown as the slope of ln[M]/[M]0

M n,A/B = F

[A]0 [B]0 M 0,A + M 0,B [CTA] [CTA]

(2)


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Figure 8. Master curve data for all materials investigated, reported as elastic modulus (Pa) versus freqency (ωaT) at a reference temperature of Tref = 55 °C. Each window has all four polymers of a specific composition: upper-left (1), upper-right (2), bottom-left (3), and bottom-right (4). The slopes of the terminal responses for selected materials are indicated with tangents.

subsequently scattering length densities between H (ca. 9.16 × 10−6 Å−2), O (ca. 8.23 × 10−6 Å−2), and M (ca. 8.61 × 10−6 Å−2) also contributed to the broadness of the scattering peaks observed in Figure 7. A large number of hexagonally packed column (H) structures were observed across the compositions, with 9 of the 16 materials indicating this structure. Figure 7 outlines all 16 SAXS traces; each panel shows each of the four architectures at a single composition. Peak reflections are indicated with a black arrow and number indicating the q/q* location of the peak. SAXS for composition 1 is in the top left panel of Figure 7. Polymers HM/O‑1, HMO-1, and H/MO-1 all have scattering reflections q/q* = 1, √3, and √4. Polymer HMO-1 shows only a primary peak with no higher-order reflections. At composition 2, in the top right panel of Figure 7, the spectra of HOM-2, HMO-2, and H/MO-2 all contain clearly distinguishable peaks at q/q* = 1, √3, √4. Additionally, HOM-2 and HMO-2 show scattering at q/q* = √9. HM/O‑2 displays a scattering pattern similar in character to those that we observe in many of the composition 3 materials, for which scattering data are summarized in the lower-left panel of Figure 7. HM/O‑2, HOM-3, HMO-3, and H/MO-3 all feature broad primary peaks with shoulders, indicative of two adjacent overlapping peaks. Higher-order reflections are also evident, although distinct Bragg peaks are unresolvable as significant overlap causes them to appear as one broad peak spread over a ≈0.2 nm−1 region of q-space. In these areas we have indicated where the Bragg reflections associated with an Ia3d̅ space group symmetry should appear with the black arrows and the associated q/q* ratios. Scattering for H/MO-3 indicates q/q* = 1, √3, √4. Composition (4) SAXS data appear in the lowerright panel of Figure 7. HOM-4 and H/MO-4 scatter with broad low-intensity primary peaks at higher q* ≈ 0.5 nm−1 with no

where M0,A and M0,B are the molecular weights of monomers A and B respectively, and bracketed quantities refer to initial molar concentrations. From eq 2, the expected molecular weights for the final H/M and O/M copolymers represented in Figure 6 were 14 kDa and 7 kDa respectively while the obtained Mn were 16 kDa and 10 kDa respectively, differences within the experimental and systematic errors. Finally, the composition of M in the copolymers was followed with 1H NMR. This is depicted in Figure 6c as the mole fraction of M (xM) plotted as a function of gravimetric conversion. In the O/M copolymerization, the target xM was 0.333 and the observed xM fluctuated around this value from a low of 0.283 to a high of 0.380, and a final value of 0.329. In the H/M copolymerization, the target xM was 0.182 and the observed xM fluctuated around this value from a low of 0.138 to a high of 0.246, with a final value of 0.167. Further details of this study, including the 1H NMR spectra, are discussed in the Supporting Information. The consistency of xM, independent of conversion, and the proximity to the target compositions is evidence the semibatch addition process described in the Experimental Section provided statistical copolymers for this study. Collectively, the reaction studies in Figure 6 for the copolymerizations between H/M and O/M illustrate the controlled (pseudo)living characteristic of CTA ETMP for the acrylic monomers of interest and support the use of a semibatch method for the production of these statistical copolymers. Structural Characterization. The self-assembly of the polymers was characterized with small-angle X-ray scattering (SAXS) and rheology. Table 1 displays the microstructures observed in the four architectures across the four compositions. Unfortunately, low Z contrasts prevented the imaging of these structures via TEM. The similarities in electron densities and G


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higher-order scattering. HMO-4 and HM/O-4 show q/q* = 1, √4, √7. Master curves assembled with dynamic shear rheology for all terpolymers are presented in Figure 8. Each panel presents all four architectures at one composition, with composition 1 in the top left, composition 2 in the top right, composition 3 in the bottom left, and composition 4 in the bottom right. The classical Rouse-like response for a homogeneous polymeric liquid is given by the scaling relationship G′ ∝ ω2 in the low frequency regime; it has been long recognized that in block copolymers, composition fluctuations in disordered melts and the structure of ordered melts give rise to a morphologydependent scaling exponent a such that G′ ∝ ωa.50 In Figure 8, tangent lines have been added to the graphs to help visualize the slope a of logG′ with respect to logωaT in the low frequency (terminal response) regime. Half of the materials indicate a terminal response with a slope of a = 1/3. In composition (1), HM/O-1, H/MO-1, and HMO-1 (at low temperature) have a slope of a = 1/3, while for HOM-1 a = 1/ 2. At T = 115 °C, time−temperature superposition of HMO-1 begins to fail (gray-shaded circles in Figure 8), with the liquidlike terminal response of a = 2 evident at T = 125 °C (filled circles, Figure 8). In composition 2, HOM-2, HMO-2, and H /MO-2 present a slope of a = 1/3. The elastic modulus of HM/O‑2 appears to approach a plateau as the frequency is decreased, with a ≪ 1/3, although the low torque signal precluded efforts to sample the lowest frequencies at elevated temperature, corresponding to log ωaT < −4.5. The master curves for composition 3 polymers give terminal regime responses with slopes approaching zero. The independence of modulus with respect to frequency is a solid like response and is especially pronounced in the curve for HOM-3. In composition 4, architectures HOM-4 and HM/O‑4 show a = 2 throughout the temperature range, while HMO-4 and H/MO-4 exhibit a solid-like response at low temperature through T = 135 °C, at which point time−temperature superposition fails, and the slope of the terminal response steepens and approaches a = 2.

Figure 9. Montage that illustrates the phase behavior of the H/O/M system as a function of composition and segment distribution.

HM/O-3, the slope was slightly less than 1/3, which may have been caused by the onset of cross-linking due to extended exposure to T > 150 °C temperatures. HOM-1, HOM-4, and HM/O-4 gave no indication of higher order reflection peaks in SAXS. The broad, low intensity peak of HOM-4 and HM/O-4 is characteristic of the correlation-hole scattering observed in disordered block copolymer melts, and slopes for HOM-4 and HM/O-4 in the terminal response is the liquid-like a = 2, indicating that these materials are disordered. The q* peak in the SAXS of HOM-1 is sharp enough to indicate microphase separation; the rheological data indicate that a = 1/2 in terminal response. These observations strongly support that HOM-1 is ordered, and tentatively suggest that the L phase is the structure. The L-phase is further bolstered by the near approximate relationship G′(ω) ≈ G″(ω) in the melt rheology (G″(ω) data for HOM-1 are provided in the Supporting Information). Four materials−HM/O-2, HOM-3, HMO-3, and H /MO-3−appear to form the cubic Q230 (double gyroid) phase. In SAXS experiments, these materials presented a broad primary peak with a shoulder that indexes well to q*/q = √6, √8, corresponding to Miller indicies of 211/220. The secondary peak is consistently broad, spanning the region occupied by q/q* = √20 (024), √22 (224), √24 (233), √26 (134), √30 (125), and √32 (044). The melt rheology of these materials shows a solid-like response in the low-frequency regime, which in block copolymer melts is consistent with a three-dimensional structure such as Q230. In the asymmetric composition 1, with a low composition of O (f O = 0.16) the HOM architecture morphology appears to be L. Given that d for HOM-1 is comparable to the other architectures, suggesting the degree of chain extension is similar between HOM and HM/O or H/MO, we propose there are

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DISCUSSION Combining the SAXS and rheological data allows us to make morphological assignments to the self-assemblies observed in these materials as summarized in Figure 9. The locations of the peak reflections with respect to the primary peak q*, informs us of symmetry and possible morphology.51 Similarly, the slope a of logG′ in the terminal response of a material indicates the degree of interconnections between domains and possible morphology and can be used to supplement SAXS data in the determination of the morphology. Work by Kossuth et al. put forth an association between the slope of log G′ with respect to ωaT at low frequencies.50 Specifically, the slope in the terminal regime for a disordered phase is a = 2; a = 1/2 for L phase; for H, a = 1/3; and for the highly interconnected Q230 phase (and other three-dimensional structures), the slope approaches the solid-like response, a → 0. In the studied materials, commonly observed SAXS reflections q/q* = 1, √3, √4 correspond to columns on a hexagonally packed lattice (H); the presence of these reflections were used to assign morphology. Additionally, q/ q* = √9, observed in HOM-2, HMO-2, and q/q* = √7, observed in HMO-4 and H/MO-4 are associated with H. Rheology was used to support the morphology assignment, and of the nine materials identified with H morphology (Table 1), 7 materials showed a slope of a = 1/3 in the terminal response. In H


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the phase diagram may be asymmetric compared to the universal diblock phase diagram. In composition 4, f HM = 0.31 and the material presents an inverse H structure, with columns of H/M in a matrix of O; this behavior is similar to that observed in material HM/O-3 and would be expected in traditional diblock polymers. Further understanding of the possible asymmetry in the phase diagram and the breadth of the H envelope is being sought computationally. Figure 10 presents a unified view of these results by mapping the terpolymers onto a transformed phase coordinate system

distinct H, O, and M domains, and the L stacking goes H−O− M−M−O−H. Increasing O to f O = 0.30 at composition 2 gives H, we propose this is a core−shell structure with discrete domains of M columns surrounded by O, in a matrix of H. This structure would minimize the O and M contacts and the chain conformation constraints on O and H. Increasing the O content in composition 3 to f O = 0.50 gives Q230. As we depict in Figure 9, based on the composition of HOM-3, we envision a core−shell structure where M forms the network struts, encapsulated in O with a H matrix. Finally, increasing f O to 0.69 in composition 4 produces a disordered phase, where all conformational constraints are minimized. In architecture HMO at low composition of O, the triblock self-assembles as H. Again, comparing the d with that of the diblocks, the chain extension is similar, suggesting there are discrete H, M, O domains; thus it is proposed this is another core−shell H, with columns of O, surrounded by M, in a matrix of H. In composition 2, HMO is also H, again proposed to be a core−shell H. The H structure at low compositions of O, allows the architecture HMO to minimize the O contacts and the conformation constraints on H. Upon increasing f O = 0.50 (composition 3), a cubic Q230 is observed. This is similar phase behavior as observed in HOM-3, where a core−shell gyroid structure of H is surrounded by M, in a matrix of O. This, again minimizes O contacts while balancing the need to minimize the conformation constraints for both O and H. At high composition of O an inverse H structure is observed, here the O makes the matrix. A drop in d suggest chain extension has decreased, indicating the H and M domains are intermixing, so we propose the columns consist of a mix of H and M. The intermixing of H and M helps to minimize the conformational constraints, while the H structure helps to minimize the O contacts and the conformation constraints on O. Turning to the diblock architectures, we expect a correlation with the diblock universal phase diagram, where the domain volume fraction can be estimated as f HM ≈ f H + f M and f OM ≈ f O + f M. Considering architecture HM/O, at low O composition, the O/M domain fraction is fixed to f OM = 0.32. Here an H structure is observed where the O/M block makes columns in a matrix of H. This phase behavior minimizes the confirmation constraints on the majority H block and is consistent with what would be expected in traditional diblock polymers.2 In composition 2, with f OM = 0.46, the morphology shifts to Q230. In the asymmetric HM/O-3 (f OM = 0.66) the progression to an O-matrix H is observed. A disordered state is produced when f OM = 0.85 in HM/O-4. The phase behavior of architecture HM/O is consistent with what would be expected from diblock polymers in the weak segregation regime across the compositions studied here. To better understand how the phase behavior of this architecture could be predicted, current efforts are focused on capturing the observed phenomena computationally. The first two compositions (1, 2) in architecture H/MO produce H with columns of O in a matrix of H/M. The f HM in these compositions are 0.84 and 0.70 respectively. That H/MO self-assembles as H at f HM = 0.84, suggest the H envelope is quite large, possibly asymmetric. Further increasing the composition of O, H/MO-3 assembles as the cubic Q230, similar to the two triblock architectures. Here minimizing both the conformation constrains for the H/M domain and the O domain produces a traditional double gyroid structure. The block fractions are symmetric with f HM = 0.50, this behavior suggests the material falls in the weak segregation regime and

Figure 10. Phase diagram of the HOM, HMO, HM/O, and H/MO architectures as described by the f */χeffN phase coordinates which map the terpolymers to a “diblock copolymer” equivalent point in phase space. Symbols are enumerated according to their chemical composition (Table 1) and connected by a curve to tie together polymers of the same architecture. While the appropriate definition of f * is straightforward for diblock terpolymers (solid symbols, solid lines), it may be elusive for triblock copolymers (transparent symbols, dotted lines). The shaded envelope represents the self-consistent mean-field theoretic binodal line for diblock copolymers.

described by a single effective volume fraction, f * and interaction strength χeffN. Such a mapping is possible in architectures where the self-assembly is dominated by a single interface. This is clearly the case for diblock terpolymers HM/O and H/MO, where phase separation occurs only between the pure block and the copolymerized block. For HM/O, f * = f H and for H/MO, f* = f H + f M. The effective interaction parameter can be estimated by eq 3, which results from equating the disordered state free energy of the diblock equivalent system, FdiskBT = f *(1 − f *)χeff, equal to that of the real system, FdiskBT = f H f MχHM + f H f OχHO + f O f MχOM. χeff =

fH fM χHM + fH fO χHO + fO fM χOM f *(1 − f *)

(3)

The phase diagram, Figure 10, produced for our diblock terpolymers using this parametrization shows good qualitative agreement between the expectations of classical diblock copolymers in the intermediate segregation regime2 and what is observed. A broad region of H-matrix columns is seen over a span of f* from 0.68 (HM/O-1) to 0.84 (H/MO-1). In H deficient polymers, a region of O-matrix columns contains HM/O-3 ( f* = 0.34); this columnar phase presumably persist to the ODT as the very weakly segregated H/MO-4 ( f * = 0.31) is included. The disordered HM/O-4 illustrates that these systems have ODT boundaries qualitatively similar to traditional diblocks. We find that Q230 forms in two symmetric I


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compositions, HM/O-2 ( f *=0.54) and H/MO-3 ( f * = 0.50), rather than the lamellar phase, which indicates a strong asymmetry in the phase diagram. Parameterization of the triblock architectures to approximate diblock architectures proves more difficult. Considering first HOM, it stands to reason that the relatively strong H/O interface should dominate the phase separation in this sequence, at least given that the M concentration is small in the materials considered in the present article. This suggests that the mapping f * = f H provide behavior consistent when compared with the diblock terpolymer mappings as plotted in Figure 10. Evidently this consistency exists, with the exception of HOM-1, which appears to be a lamellar material. Whether the inconsistency of HOM-1 with the diblock terpolymers is due to the proximity of the composition to the lamellar window (which we did not observe elsewhere in the investigated compositions) or a mis-assignment due to an absence of more conclusive scattering data is unclear. HMO, on the other hand, features two energetically balanced interfaces. This distinction suggests that only for trivial concentrations of one of the components should this sequence be mappable in any sense to a “diblock-equivalent” parameter space. However, in the HMO materials considered herein, the phase behavior of HMO mirrors that of H/MO, suggesting possible potential for a simplification of the HMO phase space to a “diblock system” with f * = f H + f M. However, there is no a priori rationale for this mapping and the similarities in the HMO/H/MO materials is coincidental, in the sense that the underlying energetic aspects leading to these morphologies are substantially different. A larger sampling of the stable morphologies with changing composition will fill in the extent to which this observation is coincidental; work in forthcoming papers explores the phase space of these triblock terpolymers at additional compositions to help further develop any “diblock system” simplifications.

block copolymer formulation, and present a simple unifying framework to aid the process of rational design.

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ASSOCIATED CONTENT

S Supporting Information *

Synthetic details, representative 1H NMR data used for the production of Figure 6, and full master curve for HOM-1 that includes both G′(ω) and G″(ω). This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*(E.W.C.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.M.H. and J.A.B. are grateful for support from the Department of Energy, Office of Basic Energy Sciences, Early Career Research Program (DE-SC0003927). E.W.C. acknowledges financial support from NSF-DMR-0847515. Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. This work was also supported in part by the MRSEC Program of the National Science Foundation under Award Number DMR0819885.

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CONCLUSION This work explores the phase behavior of hydroxyethyl acrylate (H), octyl acrylate (O), and methyl acrylate (M) terpolymers in four different architectures. ODT temperatures of the symmetric diblock copolymers between the monomers were measured and used to estimate three binary interaction parameters, yielding χHO ≈ 2χMO ≈ 2χHM. Diblock terpolymer architectures HM/O and H/MO, and triblock architectures, HOM and HMO, were synthesized with RAFT at four different compositions and the phase behavior of the 16 materials was characterized with synchrotron SAXS and dynamic shear rheology. The diblock terpolymer architectures in every case produced different morphologies at identical chemical composition. The partial phase diagram assembled by mapping these terpolymers to a “diblock-equivalent” parameter space had the familiar topology of classical diblock copolymers, with a strong asymmetric skew to H-lean compositions. Arguments based on the energetic contribution of the two interfaces in the triblock copolymer sequence HOM suggested a similar mapping, that is, essentially neglecting the contribution of the O/M interface. This approximation proved to be consistent for all but HOM-1. The HMO sequence, however, has no meaningful “diblock-equivalent” mapping although its phase behavior is nearly identical to that of the diblock copolymer sequence H/MO. Collectively, these results illustrate the utility of the segment distribution in the selection of morphology in J


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Thermodynamics of Chain Architecture in Acrylic Block Terpolymers

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