Low N, Broad Dispersity ABA Triblock

Aug 21, 2017 - triblock polymer melts using temperature-dependent SAXS, we find that broad B segment dispersity increases the minimum segregation ...
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Order and Disorder in High χ/Low N, Broad Dispersity ABA Triblock Polymers Adam K. Schmitt† and Mahesh K. Mahanthappa*,†,‡ †

Department of Chemistry, University of WisconsinMadison, 1101 University Ave., Madison, Wisconsin 53706, United States Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. S.E., Minneapolis, Minnesota 55455, United States

‡

ABSTRACT: Using a combination of small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM), we document the composition-dependent morphologies of 39 new poly(lactide-block-1,4-butadiene-block-lactide) (LBL) block polymers, comprising a broad dispersity B segment (Mn = 4.5−17.7 kg/ mol; Đ = Mw/Mn = 1.72−1.88) and narrow dispersity L end blocks (Mn = 0.6−15.3 kg/mol; Đ = 1.10−1.21) with volume fractions 0.26 ≤ f B ≤ 0.95. A subset of these samples undergo melt selfassembly into cylindrical, lamellar, and apparently bicontinuous morphologies. By assessing the states of order and disorder in these triblock polymer melts using temperature-dependent SAXS, we find that broad B segment dispersity increases the minimum segregation strength χN ≳ 27 required for LBL triblock self-assembly relative to the self-consistent mean-field theory prediction χN ≥ 17.9 for narrow dispersity analogues. While B segment dispersity has previously been shown to thermodynamically stabilize the self-assembled morphologies of low χ/high N ABA triblocks, the present study indicates that broad B block dispersity in related high χ/low N systems destabilizes the microphase-separated melt. These observations are rationalized in terms of recent theories that suggest that broad segmental dispersity substantially enhances fluctuation effects at low N, thus disfavoring melt segregation.

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molar mass dispersity (Đ ≈ 1.3−2.0) is a new molecular parameter for manipulating AB diblock and ABA triblock polymer self-assembly.12−20 For A/B copolymers, segmental dispersity alters the locations of both the compositiondependent mesophase windows and the order−disorder transition temperature (TODT), above which the microphaseseparated morphology melts into a disordered fluid.14 In the specific case of poly(styrene-block-1,4-butadiene-block-styrene) (SBS) materials with narrow dispersity S (Đ ≤ 1.25) and broad dispersity B (Đ ≈ 1.7−2.0) segments, the lamellar composition windows is asymmetrically shifted to f B = 0.52−0.75, the observed microdomain spacings nearly double, and the minimum χN required for microphase separation decreases, as compared to narrow dispersity analogues.18,19 SCMFT qualitatively captures these effects, although quantitative disagreements between experiments and theory remain with respect to the value of the minimum χN required for melt segregation.21 Functional AB and ABA block polymers used as templates for nanolithography, 22−24 molecular separations membranes,25−27 and ion transporting media28−31 often comprise highly immiscible segments (with high χ values) with low overall degrees of polymerization (N). Of particular interest in

INTRODUCTION New polymer synthesis methodologies provide exciting opportunities for the design and construction of specialty block polymer materials, which self-assemble into technologically relevant nanoscale morphologies.1−3 Expanding the utility of these materials necessitates a detailed understanding of the molecular parameters that influence their thermodynamic phase behaviors. In narrow dispersity AB diblock4−7 and ABA6,8,9 triblock polymers (Đ = Mw/Mn ≲ 1.1), ordered phase selection and stability are governed by the polymer composition fA = 1 − f B and the segregation strength χN, where N is the segment density-normalized degree of polymerization and χ is the temperature-dependent effective interaction parameter that quantifies the unfavorable A/B monomer contact energy. Self-consistent mean-field theory (SCMFT) predicts that conformationally symmetric and monodisperse ABA triblocks with χN ≥ 17.9 order into lamellar mesophases with flat interfaces when f A = 0.35−0.65,6,8 a result that was experimentally verified by Mai et al.9 Asymmetric A/B block polymer compositions drive the formation of network phases (e.g., double gyroid), hexagonally-packed cylinders, and spherical morphologies.7,10 Syntheses of new, multifunctional block polymers for advanced technologies often depend on new polymerization techniques, some of which introduce substantial molar mass dispersity into the component homopolymer segments.1,2,11 Several recent reports suggest that broad, continuous segmental © XXXX American Chemical Society

Received: July 7, 2017 Revised: August 21, 2017

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DOI: 10.1021/acs.macromol.7b01452 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules these applications are so-called “high χ/low N” block polymers that exhibit domain spacings d ≤ 20 nm, especially, those with sub-10 nm lamellar half-pitches.24 Meijer and co-workers recently reported that minute amounts of segmental dispersity in compositionally symmetric, high χ/low N poly(dimethylsiloxane-block-lactide) diblock co-oligomers stabilize their microphase-separated structures.32 However, a closely related study by Hawker and co-workers demonstrates that similarly small amounts of segmental dispersity in high χ/low N poly(methyl methacrylate-block-lactide) co-oligomers destabilize the their melt ordered morphologies.33 These apparently contradictory findings motivate further studies of the influence of segmental dispersity on block polymer self-assembly in high χ/low N systems. We previously reported the synthesis and phase behavior of 11 poly(lactide-block-1,4-butadiene-block-lactide) (LBL) triblock polymers comprising broad dispersity B blocks (Đ = 1.72−1.88) and narrow dispersity, amorphous L blocks (Đ ≤ 1.20) with compositions 0.44 ≤ f B ≤ 0.79.34 At T = 155 °C, the value of the effective χLB ≈ 0.18 is nearly 6 times greater than χSB = 0.032 for the related poly(styrene-block-1,4-butadienestyrene) (SBS) triblock polymers (vide inf ra). Consequently, these high χ/low N triblocks self-assemble into lamellar mesophases with domain spacings as small as d = 13.6 nm (lamellar half-pitch of ∼7 nm). The composition-dependent lamellar phase window for these higher χ, broad dispersity LBL triblocks was shown to shift to asymmetric compositions 0.52 ≤ f B ≤ 0.75, mirroring the aforementioned findings for disperse SBS triblocks. In accord with theoretical predictions,35 these LBL triblocks exhibit only modest domain dilation (∼3−32%) as compared to narrow dispersity LBL analogues due to their larger segregation strengths (39 ≤ χLBN ≤ 79). However, the location of the microphase separation transition (MST) and a full morphology map for this broad dispersity high χ/low N system have yet to be determined. Herein, we report the synthesis and characterization of 39 new, high χ poly(lactide-block-1,4-butadiene-block-lactide) (LBL) triblock polymers with broad dispersity B blocks and narrow dispersity, amorphous L blocks spanning the composition range 0.26 ≤ f B ≤ 0.95 with N = 125−507. Temperature-dependent small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) analyses of these samples reveal that 26 samples self-assemble into either lamellar, cylindrical, or bicontinuous melt morphologies between T = 120−180 °C, while the remaining 13 samples form disordered melts. These data enable construction of a morphology diagram for the high χ/low N broad dispersity LBL triblocks, in which the position of the microphase separation transition is identified. We specifically determine that a minimum χN ≳ 27 is required for the melt segregation of these block polymers. This unexpected thermodynamic destabilization of the microphase-separated melts driven by increased B segment dispersity in high χ/low N ABA-type triblock polymers is discussed in terms of recent theoretical developments.

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acetate, dried under vacuum, and transferred to an inert atmosphere glovebox for storage. Anhydrous and O2-free toluene was obtained by sparging analytical grade solvent with purified N2(g), followed by closed-loop recirculation over a bed of activated alumina in a Vacuum Atmospheres Co. (Hawthorne, CA) solvent purification system. 1 H NMR Spectroscopy. 1H NMR spectra were acquired in CDCl3 using a Bruker AC+ 300 spectrometer with a pulse repetition delay of 10 s to ensure quantitatively accurate peak integrations. All spectra were referenced to tetramethylsilane (TMS, (CH3)4Si). Size-Exclusion Chromatography (SEC). SEC analyses in tetrahydrofuran (THF) employed a Viscotek GPCMax system with two Polymer Laboratories Resipore separation columns (250 mm × 4.6 mm) and a differential refractive index detector, using an eluent flow rate of 0.8 mL/min at 40 °C. A polystyrene molecular weight calibration curve was constructed using 10 commercially available, narrow molecular weight standards with 580 ≤ Mn ≤ 377 400 g/mol (Polymer Laboratories, Amherst, MA). For each poly(1,4-butadiene) (B) homopolymer sample, Mn and Đ = Mw/Mn were determined using the poly(styrene) (PS) calibration curve that was Mark−Houwink corrected to poly(1,4-butadiene).36 Apparent Đ values for all LBL triblock polymers L homopolymers, where applicable, are reported against polystyrene standards without correction. Small-Angle X-ray Scattering (SAXS). Temperature-dependent synchrotron SAXS characterization was carried out at the 5-ID-D beamline of the DuPont−Northwestern−Dow Collaborative Access Team (DND-CAT) of the Advanced Photon Source (Argonne, IL). 2D-SAXS patterns were acquired with a MAR-CCD detector (133 mm diameter active circular area with 2048 × 2048 pixel resolution), using 17 keV X-rays (λ = 0.729 Å). The sample-to-detector distance was either 3.067 or 2.797 m, as determined using a silver behenate calibration standard (d = 58.38 Å). Polymer powder samples were thermally equilibrated in sealed aluminum DSC pans at each desired temperature for 5 min using a Linkam hot stage (±3 °C temperature control), prior to X-ray exposure for ∼2 s. Temperature ramp experiments were conducted between T = 80−200 °C. Lab source SAXS measurements were made using a Rigaku SMAX3000 High Brilliance Instrument, equipped with a Rigaku Micromax 002+ source from which Cu Kα X-rays (λ = 1.54 Å) were collimated with a Max-Flux multilayer confocal optic and by passage through three pinholes. Samples were thermally equilibrated using a Linkam hot stage for ∼10 min within an evacuated sample environment (±5 °C temperature control), prior to X-ray exposure for ∼3−5 min. 2DSAXS patterns were recorded on a Gabriel X-ray detector (12 cm diameter, circular active area) using either a 1 or 2 m sample-todetector distance. Temperature ramp experiments were conducted in the range T = 80−200 °C. All 2D SAXS patterns were azimuthally integrated to yield onedimensional intensity (I) versus scattering wavevector (q) scattering profiles, which were analyzed using freely available Igor Pro procedure files developed by Schmitt et al.37 Transmission Electron Microscopy (TEM). Copolymer samples were cryo-sectioned with a DiATOME diamond knife (Hatfield, PA) at −120 °C using a Leica UltraMicrotome to furnish thin samples (thicknesses ∼80−100 nm), which were transferred to copper TEM grids (400 mesh). The poly(1,4-butadiene) segments in these samples were selectively stained by a 1 h exposure to the vapor over a 4 wt % OsO4(aq) solution. TEM micrographs were obtained using a LEO 912 EFTEM operating at 120 kV. Polymer Synthesis. A detailed procedure for the synthesis of broad dispersity LBL triblock polymers was reported in our earlier paper,34 and thus we only briefly outline the approach here. Broad dispersity, telechelic α,ω-dihydroxy-poly(1,4-butadiene) (PB(OH)2) samples were obtained by a two-step procedure. First, we conducted a ring-opening metathesis polymerization of CDT in the presence of cis1,4-acetoxy-2-butene (CDAB) mediated by a Grubbs secondgeneration ruthenium catalyst in toluene to produce disperse α,ωdiacetoxy-poly(1,4-butadiene). A ratio [CDAB]:[Ru] > 90 was used in these reactions to maximize the resulting telechelic chain-end functionality (Fn → 2). Reaction of the resulting polymer with potassium ethoxide in EtOH/THF removed the acetate end groups to

EXPERIMENTAL METHODS

Materials. All reagents were obtained from the Sigma-Aldrich Chemical Co. (Milwaukee, WI) and used directly, unless otherwise noted. trans,trans,cis-1,5,9-Cyclododecatriene (CDT) was purified by vacuum distillation. Diazabicyclo[5.4.0]undec-7-ene (DBU) and cis1,4-diacetoxy-2-butene were each rendered anhydrous by vacuum distillation from CaH2. rac-Lactide was recrystallized from ethyl B

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Macromolecules reveal their hydroxyl termini. Upon isolation of the PB(OH)2 by precipitation in CH3OH and subsequent vacuum filtration, it was freeze-dried from C6H6 to remove water and any residual solvents. Mn and Đ for each PB(OH)2 used in this study are given in Table 1.

ruthenium catalyst, ring-opening metathesis polymerization (ROMP) of 1,5,9-cyclododecatriene (CDT) in the presence of varying amounts of the acyclic olefin chain transfer agent cis1,4-diacetoxy-2-butene (CDAB) afforded five α,ω-diacetoxypoly(1,4-butadienes) with different molecular weights.40 Subsequent saponification of the terminal ester moieties unmasked the terminal hydroxyl functionalities to yield five α,ω-dihydroxy-poly(1,4-butadienes) (PB(OH)2) with Mn,SEC = 4.5−17.7 kg/mol and Đ = 1.72−1.88 (Table 1). Quantitative 1 H NMR end group analyses of each PB(OH)2 enabled calculation of its number-average molecular weight Mn,NMR, which agrees within ±13% with the Mn,SEC obtained by SEC analysis. This level of agreement furnishes strong evidence for a high degree of allylic alcohol chain end functionality (Fn ≈ 2.0) in each telechelic PB(OH)2.41 The hydroxyl termini of the PB(OH)2 then served as macroinitiators for the DBUcatalyzed, living ring-opening polymerization (ROP) of raclactide38 to yield the desired disperse LBL triblock polymers. By this method, we produced 39 unimodal yet broad dispersity LBL triblock polymers (Table 2). Block polymer compositions and Mn,L for the L end segments were determined by quantitative 1H NMR spectroscopy based on Mn,SEC for the parent PB(OH)2. Chemical compositions were converted to volume fractions using the melt homopolymer densities ρL = 1.154 g/cm3 and ρB = 0.826 g/cm3 at 140 °C.42,43 Thus, the polymer compositions spanned f B = 0.26−0.95 with Mn,L = 0.6−15.3 kg/mol. Ruthenium-catalyzed olefin cross-metathesis degradation of six representative LBL samples with excess 1hexene allowed the isolation of the L end blocks,34 which exhibit Đ ≤ 1.21 by SEC against polystyrene standards. Hereafter, each polymer sample is labeled LBL-X−Y, where X denotes the overall molecular weight in kg/mol and Y is the B block volume fraction f B. Order and Disorder in the Lamellar Mesophase Window. We initially sought to probe the self-assembly thermodynamics of broad dispersity LBL triblocks within the previously identified lamellar mesophase window spanning f B ≈ 0.52−0.75, wherein samples with Mn,total ≥ 12.4 kg/mol remain melt microphase separated with TODT > 200 °C.34 Temperature-dependent SAXS analyses were not typically conducted above 200 °C due to concerns regarding thermal degradation of the L end blocks. Consequently, we targeted the synthesis of 12 disperse LBL triblocks with lower overall molecular weights in an effort to render TODT accessible (Table 2). SAXS analyses of the resulting samples at T ≥ 120 °C revealed that triblocks with Mn,total ≤ 10.0 kg/mol and f B = 0.52−0.79 exhibit only a broad, low intensity scattering peak with no higher order maxima. This SAXS signature is consistent with the correlation-hole scattering arising from a disordered (DIS) block polymer melt.44 However, a small increase in the total molecular weight of the polymer leads to microphase separation. For example, SAXS patterns of LBL-10.4−53 in Figure 1 displays sharp scattering maxima located at q* and 2q* (q* = 0.0483 Å−1 or d* = 13.0 nm) consistent with Bragg scattering from an ordered high χ/low N lamellar (LAM) block polymer mesophase when T ≤ 140 °C. Increasing the temperature to 150 °C causes these sharp SAXS peaks to weaken, and broad, low intensity correlation-hole scattering of a disordered block polymer melt develops. Note that at 150 °C the synchrotron SAXS pattern for LBL-10.4−53 apparently exhibits some degree of coexistence of the ordered and disordered phases. However, similar coexistence is also observed in low molecular weight,

Table 1. Molecular Weights of Broad Dispersity Telechelic PB(OH)2 Segments sample

Mn,NMRa (kg/mol)

Mn,SECb (kg/mol)

Đb

PB(OH)2-4.5 PB(OH)2-4.6 PB(OH)2-6.6 PB(OH)2-7.9 PB(OH)2-13.3 PB(OH)2-17.7

5.1 4.4 7.0 n.d.c 13.7 15.4

4.5 4.6 6.6 7.9 13.3 17.7

1.88 1.84 1.73 1.88 1.72 1.76

a

Calculated from quantitative 1H NMR end group analysis in CDCl3 using the allylic alcohol end group signals. bDetermined by SEC analysis in THF using polystyrene calibration, which was Mark− Houwink corrected for poly(1,4-butadiene).36 cn.d. = not determined. Disperse LBL triblock polymers were synthesized by initiating organocatalytic ring-opening polymerization of rac-lactide from the hydroxyl ends of telechelic PB(OH)2 samples in toluene using DBU as a catalyst. Per a previous report by Lohmeijer et al.,38 we used [lactide]:[DBU] = 100:1. These living polymerizations produce narrow dispersity, amorphous L end blocks, the chemical degrees of polymerization of which are set by NL = [lactide]/2·[PB(OH)2]. Polymer samples thus obtained were freeze-dried from C6H6 containing 0.5 wt % Irganox 1076 (relative to polymer) as a stabilizer, in order to prevent cross-linking during subsequent high temperature analyses. 1H NMR analyses were used to quantitate the polymer compositions and the end segment molecular weights (Mn,L). For a few select LBL triblocks, we confirmed the low dispersities of the L segments by direct SEC analyses using a previously described method.34 Briefly, broad dispersity LBL triblock polymers were subjected to ruthenium-catalyzed olefin cross-metathesis with excess 1hexene to degrade the B segment and enable isolation of the L end blocks. SEC analyses revealed that Đ ≤ 1.21 for these L end segments.

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RESULTS AND DISCUSSION We synthesized a series of LBL triblock polymers comprising broad dispersity B segments and narrow dispersity L end blocks, using our previously developed synthetic route depicted in Scheme 1,34 which is closely related to that reported by Pitet and Hillmyer.39 Catalyzed by Grubbs’ second-generation Scheme 1. Tandem ROMP/ROP Synthesis of Disperse LBL Triblock Polymers

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Macromolecules Table 2. Molecular and Morphological Characteristics of Broad Dispersity LBL Triblock Polymers sample

Mn,Ba (kg/mol)

ĐBa

Mn,Lb (kg/mol)

LBL-32.4−26 LBL-38.5−27 LBL-31.0−27 LBL-31.5−32 LBL-25.2−33 LBL-22.6-37 LBL-26.7−37 LBL-14.9-38 LBL-14.9−38 LBL-22.1−44 LBL-12.5−44 LBL-34.7−46 LBL-32.7−49 LBL-16.0−50 LBL-15.8−50 LBL-18.9−50 LBL-10.5−51 LBL-17.5−53 LBL-28.9−54 LBL-10.4−53 LBL-14.8−53 LBL-9.7−55 LBL-9.2−58 LBL-9.1−58 LBL-8.4−63 LBL-11.0−68 LBL-12.9−69 LBL-10.0−72 LBL-9.2−78 LBL-24.3−79 LBL-18.3−79 LBL-17.1−83 LBL-22.7−83 LBL-8.2−85 LBL-16.1−87 LBL-21.1−88 LBL-15.1−91 LBL-19.9−92 LBL-18.9−95

6.6 7.9 6.6 7.9 6.6 6.6 7.9 4.5 4.5 7.9 4.5 13.3 13.3 6.6 6.6 7.9 4.5 7.9 13.3 4.6 6.6 4.5 4.6 4.6 4.6 6.6 7.9 6.6 6.6 17.7 13.3 13.3 17.7 6.6 13.3 17.7 13.3 17.7 17.7

1.73 1.88 1.73 1.88 1.73 1.73 1.88 1.88 1.88 1.88 1.88 1.72 1.72 1.73 1.73 1.88 1.88 1.88 1.72 1.84 1.73 1.88 1.84 1.84 1.84 1.73 1.88 1.73 1.73 1.76 1.72 1.72 1.76 1.73 1.72 1.76 1.72 1.76 1.76

12.9 15.3 12.2 11.8 9.3 8.0 9.4 5.2 5.2 7.1 4.0 10.7 9.7 4.7 4.6 5.5 3.0 4.8 7.8 2.9 4.1 2.6 2.3 2.3 1.9 2.2 2.5 1.7 1.3 3.3 2.5 1.9 2.5 0.8 1.4 1.7 0.9 1.1 0.6

ĐLc

Mn,LBLb (kg/mol)

ĐLBLc

Nd

fB

χNe

morphologyf

dSAXSf (nm)

32.4 38.5 31.0 31.5 25.2 22.6 26.7 14.9 14.9 22.1 12.5 34.7 32.7 16.0 15.8 18.9 10.5 17.5 28.9 10.4 14.8 9.7 9.2 9.1 8.4 11.0 12.9 10.0 9.2 24.3 18.3 17.1 22.7 8.2 16.1 21.1 15.1 19.9 18.9

1.32 1.23 1.27 1.35 1.25 1.27 1.28 1.17 1.18 1.28 1.18 1.29 1.30 1.23 1.25 1.26 1.32 1.27 1.31 1.32 1.24 1.33 1.35 1.32 1.34 1.32 1.45 1.35 1.37 1.52 1.49 1.51 1.59 1.42 1.57 1.64 1.61 1.69 1.69

427 507 410 422 339 307 364 203 203 308 174 487 463 227 225 269 150 252 417 149 212 140 134 134 125 166 195 154 144 382 287 273 362 132 261 343 248 328 316

0.26 0.26 0.27 0.32 0.33 0.36 0.37 0.38 0.38 0.44 0.44 0.46 0.49 0.50 0.50 0.50 0.51 0.53 0.54 0.53 0.53 0.55 0.58 0.58 0.63 0.68 0.69 0.73 0.78 0.79 0.79 0.83 0.83 0.85 0.87 0.88 0.91 0.92 0.95

77 91 74 76 61 55 66 37 37 55 31 88 83 41 41 48 27 45 75 27 38 25 24 24 23 30 35 28 26 69 52 49 65 24 47 62 45 59 57

CYLB CYLB CYLB CYLB CYLB CYLB CYLB CYLB CYLB CYLB CYLB BIC BIC INT INT INT DIS INT INT LAM (155) LAM DIS DIS DIS DIS LAM (160) LAM (175) DIS DIS LAM Dis CYLL DIS Dis CYLL DIS DIS Dis CYLL DIS DIS DIS

23.0 28.6 23.4 27.5 24.2 22.6 28.6 20.1 18.5 27.5 18.3 32.5 31.8 19.0 18.7 24.6

1.12

1.10 1.15

1.12

1.21

1.10

22.3 28.0 13.0 17.3

15.6 17.0

23.8 19.3 20.1

16.8

a

Determined by SEC using PS standards (Mn = 580−377 400 g/mol) corrected for PB using Mark−Houwink parameters.36 bDetermined from quantitative 1H NMR spectroscopy using the ratio of the integrated peaks for the L and B segments along with Mn,B. cDetermined by SEC against PS standards (uncorrected). dSegment density-normalized degree of polymerization determined using Mn and the melt densities ρB = 0.826 g/cm3 and ρL = 1.154 g/cm3 at 140 °C42,43 relative to a 118 Å3 reference volume. eCalculated at 155 °C using χLB = 0.18 with respect to the 118 Å3 reference volume.34 fMorphology and domain spacing from SAXS at 120 °C; TODT (°C) is listed in parentheses if observed.

correlation-hole scattering of a disordered diblock polymer to the random phase approximation (RPA) to extract χ4,46 and (2) determination of TODT for a compositionally symmetric diblock polymer and use of the mean-field result (χN)ODT = 10.495.46−48 The effective interaction parameter is consistently estimated by both methods as χLB ≈ 0.18 in the temperature range T = 155−170 °C, using the somewhat arbitrary 118 Å3 reference volume that corresponds to the volume of a four atom repeat unit of a typical polymer such as poly(1,4butadiene).24,48 (Note that the value of χLB given in ref 34 was miscalculated due to the use of the B segment density at 298 K instead of 413 K.43) From molecular weights of the constituent homopolymer segments, we calculated N relative to the 118 Å3 reference volume using the aforementioned melt homopolymer densities. Table 2 lists the calculated magnitude of χLBN at 155

narrow dispersity polymers near their order−disorder transition temperatures;32,45 thus, it does not appear to be a unique feature of the disperse LBL samples. The sharp Bragg scattering peaks are completely extinguished, signaling a disordered polymer melt. Thus, LBL-10.4−53 exhibits an accessible TODT ≈ 155 °C. Similar behaviors were observed for LBL11.0−68 and LBL-12.9−69, which respectively exhibit TODT ≈ 160 and 175 °C. Further increasing the overall molecular weight drives the formation of lamellar morphologies with TODT > 200 °C as in LBL-14.8−53 and LBL-24.3−79 as expected. The magnitude of the effective interaction parameter χLB has already been experimentally measured by two different and accepted experimental methods,34 based on established meanfield theories for block polymer melts: (1) fitting the D

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at q/q* = 1, √3, and √4 consistent with a hexagonally packed cylinders morphology. However, the higher order peak located at q* = 0.085 Å−1 is inconsistent with this phase assignment, and the excess intensity in the range 0.04 ≤ q ≤ 0.06 Å−1 that partially masks the cylindrical mesophase scattering suggests possible two-phase coexistence. If one assumes that the principal scattering peaks for the coexisting phases overlap, the peak at q* = 0.085 Å−1 may correspond to the 3q* peak of a coexisting lamellar morphology. Samples of this polymer were cryo-sectioned at −120 °C and treated with OsO4 vapor in order to selectively stain the B segments for enhanced electron microscopy imaging contrast. Subsequent TEM analyses show a mixture of layer-like structures with circular perforations, consistent with either a defect-ridden lamellar structure or lamellae/cylinders phase coexistence (Figure 3A). Self-conFigure 1. A one-dimensional synchrotron SAXS intensity versus scattering wavevector q profile for LBL-10.4−53 at 140 °C demonstrates the formation of a lamellar phase. Increasing the temperature to 150 °C drives the gradual disappearance of the sharp SAXS peaks and evolution of broad, low-intensity correlation-hole scattering at T = 150 °C. Above the order−disorder transition temperature TODT = 155 °C, the melt exhibits only correlation-hole scattering associated with a disordered copolymer melt.

°C for each ordered and disordered LBL sample with f B = 0.51−0.79 (see Table 2). Thus, the above morphology analyses by SAXS reveal that a minimum value of χLBN ≥ 27 is required for broad dispersity LBL triblock melt microphase separation. Intermediate Phases with f B = 0.46−0.54. In the composition range f B = 0.46−0.54, we observe two different SAXS signatures depending on the overall LBL molecular weight (Table 2). When Mn,total = 15.8−18.9 kg/mol, SAXS patterns present scattering maxima that cannot be indexed to one single microphase-separated morphology. An exemplary azimuthally integrated X-ray intensity profile for LBL-18.9− 0.50 at 200 °C (Figure 2) reveals the presence of peaks located

Figure 3. Representative TEM micrographs of broad dispersity LBL triblock polymers indicating that (A) LBL-18.9−50 forms an intermediate phase in which lamellar microdomains are punctuated with circular perforations and (B) LBL-32.7−40 forms a weblike bicontinuous structure with interpenetrating L and B domains. The B domains appear dark in these images, as the samples were stained with OsO4 vapor.

sistent mean-field calculations by Matsen predict windows of equilibrium two-phase coexistence between pure phases in disperse AB diblock polymers49 and by extension ABA triblock polymers.21 However, the time scale of our experiments is likely too short to yield well-developed macrophase-separated grains due to slow polymer diffusion in the segregated melt. Within the resolution of our experiments (q ≥ 0.007 Å−1), we do not observe any low q scattering symptomatic of macrophase separation into two distinct morphologies. Thus, we are uncertain whether the morphology observed by SAXS and TEM in this composition region is kinetically trapped or if it reflects the minimum free energy state. As such, we identify these samples as intermediate (INT) phases in Table 2. For samples with Mn = 32.7−34.7 kg/mol, SAXS reveals a strong primary scattering peak along with broad higher order features that are also not consistent with any known melt segregated morphology (Figure 2). TEM analyses of OsO4stained LBL-32.7−49 sections indicate the formation of interpenetrating L and B weblike microdomain structures that are consistent with a bicontinuous (BIC) morphology (Figure 3B). The TEM micrographs and SAXS data for LBL-32.7−49 are quite similar in texture to those recorded for the disorganized bicontinuous morphology formed by broad dispersity SBS triblocks.18,19 Pitet and Hillmyer also reported the formation of similar morphologies in high molecular weight, broad dispersity LEL triblocks (E = high density poly(ethylene)) with nearly the same volume compositions.26 They directly established that their samples exhibit bicontin-

Figure 2. Azimuthally integrated SAXS patterns acquired at 200 °C for (a) LBL-18.9−50 (bottom) indicate the formation of an intermediate phase having peaks corresponding to hexagonally packed cylinders (triangles) and lamellae (circles) and (b) LBL-32.7−49 that forms a disorganized bicontinuous morphology. E

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samples form ordered structures according to our SAXS analyses (Table 2). The representative one-dimensional scattering profile for LBL-18.3−79 with two strong, broad peaks indicates a poorly ordered yet microphase-separated morphology (Figure 5A). TEM investigations divulge the

uous morphologies by chemically etching the L domains to yield useful, nanoporous high-density polyethylenes. Ordered Morphologies with f B ≤ 0.44. In contrast to the INT morphologies described above, broad dispersity LBL triblocks with f B = 0.26−0.44 order into B cylinders in a narrow dispersity L matrix phase (CYLB) with modest degrees of longrange translational order (Table 2). A sample SAXS pattern for LBL-12.5−44 (Figure 4A) exhibits peaks at q/q* = 1, √3, √4,

Figure 4. (A) Azimuthally integrated synchrotron SAXS patterns acquired at 160 °C for LBL-12.5−44 indicate the formation of hexagonally packed cylinders with good long-range order, whereas the higher molecular weight LBL-32.4−26 forms a cylindrical morphology with a lesser degree of translational order. Markers indicate the expected peak positions for the hexagonally packed cylinders morphology. TEM micrographs of (B) LBL-12.5−44 and (C) LBL32.4−26 corroborating the morphology assignments derived from SAXS analyses (B segments were stained with OsO4 and appear dark).

Figure 5. (A) Synchrotron SAXS patterns for LBL-17.1−83 and LBL18.3−79 reveal the formation of a disorganized cylinders phase, which is consistent with the (B) TEM image for LBL-18.3−79 that shows disorganized threadlike cylindrical micelles of L (white) in a B matrix, which appears dark due to sample staining with OsO4.

√9, √12, and √13. Support for this phase assignment derives from TEM micrographs of this sample (Figure 4B), in which we observed periodic arrays of dark dots consistent with hexagonally packed cylinders of B stained with OsO4. However, the degree of long-range order in these samples in this composition window significantly diminishes upon increasing the LBL molecular weight. The 1D-SAXS intensity profile for LBL-32.4−26 displays a strong principal scattering peak with only broad and weak higher order reflections (Figure 4A). TEM imaging clearly indicates the presence of discontinuous B domains in a matrix of L (Figure 4C), albeit with no obvious spatial symmetry. We tentatively identify this sample as also microphase separating into CYLB. Disorganized Cylinders: f B ≥ 0.78. Of the 10 LBL triblocks synthesized with f B ≥ 0.78 and χLBN ≤ 65, only three

formation of disorganized, threadlike L cylinders (Dis CYLL) in a dark matrix of broad dispersity B (Figure 5B), which strongly resembles the disorganized poly(styrene) cylinders in a poly(1,4-butadiene) matrix previously reported in disperse SBS triblock polymers.19A modest increase in the B segment volume fraction to f B = 0.83 as in LBL-17.1−83 also yields a segregated melt, which exhibits poor long-range order evidenced by broad SAXS peaks that appear qualitatively similar to those of LBL-18.3−79 (Figure 5a). LBL Morphology Diagram. Figure 6 summarizes the results of our LBL triblock polymer morphology analyses in the form of a χLBN versus f B phase diagram. In constructing this diagram, we used a reference temperature of 155 °C at which χLB = 0.18 relative to a 118 Å3 reference volume (vide supra), and we neglected any composition dependence in the F

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both theory and previous experiments set the expectation that B segment dispersity should decrease (χN)ODT. Aside from the shift of the MST to higher values, we note that the qualitative shape of the MST for the LBL triblocks, the observed sequence of morphologies with increasing f B, and the pronounced asymmetric shift in the lamellar phase window is similar to that of the aforementioned SBS samples. We refer the interested reader to our earlier papers17,19,34 for a conceptual rationalization of the lamellar phase window shift, in order to avoid distraction from our focus here on the location of the MST. While the noted thermodynamic destabilization of segregated melts in high χ/low N ABA triblocks with broad B segments may initially seem surprising, differences between low N and high N melts are not entirely unexpected. At low values of N, the multiblock polymer chain conformations are expected to deviate significantly from Gaussian statistics and the role of the polymer end group functionalities may become quite important.50,51 Additionally, theory and simulations demonstrate that fluctuation effects are very significant and cannot be neglected in narrow dispersity block polymers at low N.52−58 Fluctuations destabilize the self-assembled morphologies, thus increasing (χN)ODT. Pandav and Ganesan recently investigated the specific roles of molecular weight and composition dispersity on the phase behavior of AB diblocks using a modified SCMFT approach.55 Their systematic theoretical studies clearly establish that both composition and molecular weight dispersities in a diblock polymer melt amplify fluctuation effects. Furthermore, they suggest that the magnitude of these dispersity-induced fluctuations may become so large that they overwhelm the predicted dispersity-driven decrease in (χN)ODT predicted by SCMFT. Thus, (χN)ODT increases or TODT decreases. Consistent with this theoretical prediction, Hawker and co-workers recently demonstrated that small amounts of segmental dispersity in high χ/low N diblock co-oligomers measurably reduce TODT (Đ = 1.13 versus 1.001 with Mn ≤ 4.0 kg/mol; N < 100).33 One expects these effects to become stronger as the segmental dispersities Đ → 2.0. By similar reasoning, we speculate that fluctuation effects are also substantially amplified in the low N LBL triblocks considered here given that these samples exhibit both broad composition and molecular weight dispersities (N ≲ 200 for samples with accessible TODT’s). Furthermore, these fluctuations apparently override the modest dispersity-induced reduction in (χN)ODT predicted by Matsen using SCMFT. Lynd et al. have also previously noted that SCMFT predictions are quite sensitive to the detailed shapes of the molecular weight distributions of the segments in disperse diblock and triblock polymers.35 By extension, we also anticipate that the magnitude of the fluctuation correction for disperse multiblock polymers with low N are similarly sensitive and must be considered in future theoretical and experimental studies.

Figure 6. Morphology diagram for high χ/low N LBL polymers comprising broad dispersity center B blocks (Đ = 1.72−1.88) and narrow dispersity L end segments (Đ ≤ 1.21) derived from the experimental data in Table 2, in conjunction with data previously reported in ref 34, using χLB = 0.18 at a reference temperature of 155 °C. The colored regions and line delineating the apparent order− disorder boundary are guides to eye and are not necessarily exact. Observed morphologies are labeled as LAM = lamellae, CYLB = B cylinders in a matrix of L, and CYLL = L cylinders in a B matrix. BIC = bicontinuous and INT = ill-defined intermediate phase.

magnitude of χLB. This data compilation also includes the 11 lamellae-forming, broad dispersity LBL triblock polymers with compositions f B = 0.52−0.75 that were reported earlier.34 Although the number of samples reported in this diagram is large, we do not preclude the possibility that other ordered phases (including two-phase coexistence) may occur at points that were not explicitly studied. Inclusion of the 12 melt disordered samples in this diagram allows us to define the MST for samples with f B ≥ 0.52, the location of which is further supported by its proximity to the three lamellar samples that exhibit accessible TODT = 150−170 °C. In Figure 6, the line separating the ordered and disordered regions of phase space is intended to serve as a guide to the eye, and we do not imply any analytical model fit by its location. A striking feature of the LBL morphology diagram is that the minimum in the MST occurs near f B ≈ 0.53 with χN ≥ 27, thus specifying the critical criterion for disperse LBL triblock microphase separation. Since the χ parameter used to construct this morphology diagram originates from mean-field theory interpretations of the experimentally observed phase behaviors of ordered and disordered block polymers, we first compare our data to mean-field theory. For perfectly monodisperse ABA triblocks, SCMFT predicts that melt ordering requires χN ≥ 17.9.6,8 In this light, our results imply that B segment dispersity thermodynamically destabilizes ABA triblock melt ordering. The observed increase in (χN)ODT for broad dispersity LBL triblocks relative to their narrow dispersity analogues is surprising in view of earlier studies by Widin et al., which demonstrated that SBS triblocks with similarly broad B and narrow S segment dispersities only require χN ≥ 4.5 for microphase separation.18,19 Matsen’s SCMFT predictions for these disperse triblock materials also anticipate a decreased MST location, with the minimum (χN)ODT ≥ 7 for ABA triblocks upon increasing the B block ĐB → 1.5.21 However, these theoretical predictions assume Gaussian chain statistics from which one expects significant deviations at low N. Thus,

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CONCLUSION The effects of broad center segment dispersity on the selfassembly of high χ/low N poly(lactide-block-1,4-butadieneblock-lactide) triblock polymers were investigated through the chemical synthesis and physical characterization of 39 samples spanning the composition range f B = 0.26−0.95. Using a combination of SAXS and TEM analyses, we found that many of these samples microphase separate into lamellar, cylindrical, and bicontinuous morphologies in the temperature range 80− 200 °C, while the remainder form only disordered melts. The combination of these melt disordered samples and three low N G

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Diblock Copolymer Phase Diagram near the Order-Disorder Transition. Macromolecules 1995, 28, 8796−8806. (8) Mayes, A. M.; Olvera de la Cruz, M. Microphase Separation in Multiblock Copolymer Melts. J. Chem. Phys. 1989, 91, 7228−7235. (9) Mai, S.-M.; Mingvanish, W.; Turner, S. C.; Chaibundit, C.; Fairclough, J. P. A.; Heatley, F.; Matsen, M. W.; Ryan, A. J.; Booth, C. Microphase-Separation Behavior of Triblock Copolymer Melts. Comparison with Diblock Copolymer Melts. Macromolecules 2000, 33, 5124−5130. (10) Abetz, V.; Simon, P. F. W. Phase Behaviour and Morphologies of Block Copolymers. AdV. Polym. Sci. 2005, 189, 125−212. (11) Lodge, T. P. Block Copolymers: Past Successes and Future Challenges. Macromol. Chem. Phys. 2003, 204, 265−273. (12) Bendejacq, D.; Ponsinet, V.; Joanicot, M.; Loo, Y. L.; Register, R. A. Well-Ordered Microdomain Structures in Polydisperse Poly(Styrene)-Poly(Acrylic Acid) Diblock Copolymers from Controlled Radical Polymerization. Macromolecules 2002, 35, 6645−6649. (13) Ruzette, A.-V.; Tence-Girault, S.; Leibler, L.; Chauvin, F.; Bertin, D.; Guerret, O.; Gerard, P. Molecular Disorder and Mesoscopic Order in Polydisperse Acrylic Block Copolymers Prepared by Controlled Radical Polymerization. Macromolecules 2006, 39, 5804−5814. (14) Lynd, N. A.; Meuler, A. J.; Hillmyer, M. A. Polydispersity and Block Copolymer Self-Assembly. Prog. Polym. Sci. 2008, 33, 875−893. (15) Lynd, N. A.; Hillmyer, M. A. Effects of Polydispersity on the Order-Disorder Transition in Block Copolymer Melts. Macromolecules 2007, 40, 8050−8055. (16) Li, S.; Register, R. A.; Weinhold, J. D.; Landes, B. G. Melt and Solid-State Structures of Polydisperse Polyolefin Multiblock Copolymers. Macromolecules 2012, 45, 5773−5781. (17) Schmitt, A. L.; Mahanthappa, M. K. Polydispersity-Driven Shift in the Lamellar Mesophase Composition Window of PEO-PB-PEO Triblock Copolymers. Soft Matter 2012, 8, 2294−2303. (18) Widin, J. M.; Schmitt, A. K.; Im, K.; Schmitt, A. L.; Mahanthappa, M. K. Polydispersity-Induced Stabilization of a Disordered Bicontinuous Morphology in ABA Triblock Copolymers. Macromolecules 2010, 43, 7913−7915. (19) Widin, J. M.; Schmitt, A. K.; Schmitt, A. L.; Im, K.; Mahanthappa, M. K. Unexpected Consequences of Block Polydispersity on the Self-Assembly of Aba Triblock Copolymers. J. Am. Chem. Soc. 2012, 134, 3834−3844. (20) Hustad, P. D.; Marchand, G. R.; Garcia-Meitin, E. I.; Roberts, P. L.; Weinhold, J. D. Photonic Polyethylene from Self-Assembled Mesophases of Polydisperse Olefin Block Copolymers. Macromolecules 2009, 42, 3788−3794. (21) Matsen, M. W. Comparison of A-Block Polydispersity Effects on BAB Triblock and AB Diblock Copolymer Melts. Eur. Phys. J. E: Soft Matter Biol. Phys. 2013, 36, 44. (22) Bang, J.; Jeong, U.; Ryu, D. Y.; Russell, T. P.; Hawker, C. J. Block Copolymer Nanolithography: Translation of Molecular Level Control to Nanoscale Patterns. Adv. Mater. 2009, 21, 4769−4792. (23) Bates, C. M.; Maher, M. J.; Janes, D. W.; Ellison, C. J.; Willson, C. G. Block Copolymer Lithography. Macromolecules 2014, 47, 2−12. (24) Sinturel, C.; Bates, F. S.; Hillmyer, M. A. High χ-Low N Block Polymers: How Far Can We Go? ACS Macro Lett. 2015, 4, 1044− 1050. (25) Phillip, W. A.; Rzayev, J.; Hillmyer, M. A.; Cussler, E. L. Gas and Water Liquid Transport through Nanoporous Block Copolymer Membranes. J. Membr. Sci. 2006, 286, 144−152. (26) Pitet, L. M.; Amendt, M. A.; Hillmyer, M. A. Nanoporous Linear Polyethylene from a Block Polymer Precursor. J. Am. Chem. Soc. 2010, 132, 8230−8231. (27) Reijerkerk, S. R.; Wessling, M.; Nijmeijer, K. Pushing the Limits of Block Copolymer Membranes for CO2 Separation. J. Membr. Sci. 2011, 378, 479−484. (28) Weber, R. L.; Ye, Y.; Schmitt, A. L.; Banik, S. M.; Elabd, Y. A.; Mahanthappa, M. K. Effect of Nanoscale Morphology on the Conductivity of Polymerized Ionic Liquid Block Copolymers. Macromolecules 2011, 44, 5727−5735.

samples that exhibit accessible order−disorder transitions between T = 150−170 °C enabled the determination of the minimum segregation strength required for melt microphase separation as χN ≳ 27. This experimental result demonstrates that increasing the dispersity of the center segment of a low N ABA-type triblock polymer increases the free energy of the microphase separated melt as compared to that of a narrow dispersity material. This dispersity-induced destabilization of the self-assembled block polymer morphology likely arises from amplified fluctuations in low molecular weight, broad dispersity materials. These studies highlight the importance of polymer synthesis methods that enable access to high precision block polymer materials with low N for future technological applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel (612) 625-4599. ORCID

Mahesh K. Mahanthappa: 0000-0002-9871-804X Present Address

A.K.S.: The Dow Chemical Company, S. Saginaw Rd., Midland, MI 48640. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge financial support from the National Science Foundation (DMR-1307606 and DMR-1631598). This work also relied on critical core instrumentation facilities funded in part by NSF grants (CHE-9974839) and the University of Wisconsin NSEC (DMR-0832760) and CEMRI (DMR-1121288), which are part of the NSF-funded Materials Research Facilities Network. Synchrotron SAXS analyses were conducted at the DuPont−Northwestern−Dow Collaborative Access Team (DND-CAT) beamline located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by Northwestern University, E.I. DuPont de Nemours & Co., and The Dow Chemical Company. This research 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.

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