Power Law Relaxations in Lamellae Forming Brush Block Copolymers

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Power Law Relaxations in Lamellae Forming Brush Block Copolymers with Asymmetric Molecular Shape Benjamin M. Yavitt,† Hua-Feng Fei,† Gayathri N. Kopanati,† H. Henning Winter,*,†,‡ and James J. Watkins*,† †

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Department of Polymer Science and Engineering, University of Massachusetts Amherst, 120 Governors Drive, Amherst, Massachusetts 01003, United States ‡ Department of Chemical Engineering, University of Massachusetts Amherst, 686 N. Pleasant Street, Amherst, Massachusetts 01003, United States S Supporting Information *

ABSTRACT: We report the linear viscoelasticity of densely grafted poly(styrene)-block-poly(ethylene oxide) (PS-b-PEO) diblock bottlebrush block copolymers (dbBB) of equal mass fraction over a wide range of backbone degree of polymerization (Nbb = 21−119). The difference in side chain length (PS Mn = 2.9 kg/mol, PEO Mn = 5 kg/mol) produces an asymmetry between the molecular shape of the two blocks despite their equal mass fractions. The dbBBs rapidly self-assemble into lamellar morphologies upon thermal annealing. Increasing Nbb results in an increase of domain spacing from d0 = 29 to 90 nm. In the microphase separated melt state, dbBBs are thermorheologically simple and remain unentangled up to large molecular weight (Mw > 500 kg/mol). Oscillatory shear rheology data shows distinct power law relationships analogous to critical gels across a wide range of time scales. The viscoelasticity is expressed by a dual power law relaxation time spectrum H(τ), consisting of relaxation processes at short (n1) and long (n2) time scales. Scaling on short time scales (n1 ≈ 0.83) is attributed to the cooperative mobility of internal slip layers (ISLs) confined within the microphase separated domains. Slipping is facilitated by a high concentration of free chain ends in the middle of each domain. Longer time scales (n2 ≈ 0.67) are dominated by the microphase separation, which is globally disordered. The results suggest a weakly percolating structure with rapid dynamic rearrangements of bottlebrushes within the PS/PEO interface.

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INTRODUCTION Block copolymers (BCPs) of uniform block lengths are wellknown for their ability to self-assemble into periodic nanoscale structures.1,2 Despite the great advances toward understanding the fundamentals that drive structure and microphase segregation, there has been less success in harnessing their periodic nature for use in applications that require rapid selfassembly and large lattice spacing.3 Microphase separated linear block copolymers (LBCPs) may take hours or even several days of annealing to achieve acceptable well-ordered states, which is often too time-consuming for large-scale fabrication processes. The slow ordering dynamics are primarily due to kinetic constraints caused by chain entanglements, which become increasingly significant as the molecular weight (MW) increases.2 Slow dynamics at high MW effectively limits the achievable domain spacing of structures in LBCPs to less than 100 nm for most systems. Alternative architectures of block copolymer, such as the brush block copolymer (BBCP), have shown great promise in alleviating many of the barriers to rapid self-assembly.4−8 AB diblock bottlebrushes (denoted as “dbBB”) are macromolecules with two discrete block segments, each possessing their own type of polymeric side chain densely grafted to a © XXXX American Chemical Society

molecular backbone. Precise synthetic approaches have resulted in polymers of uniform side chain length at very high grafting density.8,9 Extended backbone conformations arise due to steric repulsion between grafted side chains, resulting in high mobility in the melt that facilitates the rapid self-assembly.10−14 Additionally, dbBBs are proven to be effective templates for the development of functional nanomaterials. Recent examples include the ordered assembly of large nanoparticles into lamellar and cylindrical arrays, porous materials with tunable spacings, and photonic crystal resins and coatings exhibiting structural color.6,7,15−18 The densely grafted brush motif directly impacts the chain dynamics and rheological properties of both homopolymer bottlebrushes (hBB) and dbBBs.19−25 For example, in hBBs with poly(norbornene)-based backbone and short side chains, the entanglement plateau in storage modulus G′(ω) can be suppressed up to exceptionally large overall Mw (∼1000 kg/ mol) due to extended backbone conformations induced by the dense grafting of side chains.21,22,25 The overall length of the Received: August 27, 2018 Revised: December 21, 2018

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DOI: 10.1021/acs.macromol.8b01843 Macromolecules XXXX, XXX, XXX−XXX

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reports.7 Additional synthesis and experimental details are available in the Supporting Information. The overall molecular weight of the dbBB was varied while keeping the mass fraction of the two blocks constant and equal (50/50 wt %). Absolute molecular weights of dbBBs were determined by GPC-Multi Angle Laser Light Scattering (MALLS). The weight-average molecular weight (Mw) was controlled over a wide range from Mw = 86 to 560 kg/mol (Figure S2b). While the overall composition of the dbBBs is symmetric, there are additional asymmetries to consider between each block. For example, the ratio of the calculated block backbone length is asymmetric (Nbb-PS/Nbb-PEO ≈ 1.6). The asymmetry accommodates the significant difference in side chain length between each block (Nsc‑PS = 28, Nsc‑PEO = 114) while maintaining equal mass ratio. The backbone lengths produce an asymmetric “molecular shape” within the diblocks (Figure 1). On the PS side, Nsc‑PS ≤ Nbb‑PS and the molecular shape

backbone (Nbb) dictates the behavior at longer relaxation times (i.e., lower frequency).22,25 While the backbones behave as semiflexible chains, the relaxation process can be modeled by Zimm and Rouse-like dynamics, as shown by Dalsin et al. for unentangled atactic poly(propylene) (aPP) hBBs and entangled poly(ethylene-alt-propylene) (PEP) hBBs with long side chains.22 Power law scaling in frequency dependent complex viscosity (η*(ω) ∼ ωx) of x = −0.33 (Zimm) and x = −0.5 (Rouse) was identified within the intermediate frequency regime. While the models were initially developed to describe the dynamics of flexible, linear polymer chains in dilute solution, the qualitative picture and quantitative scaling of each model are useful in describing the dynamics of hBB melts. Recent studies have revealed that the hBB backbone begins to entangle at exceptionally large backbone degree of polymerizations (Nbb > 1000), as reptation dynamics set in.21 The relaxation processes in microphase separated materials (both linear and brush) are quite different from homogeneous melts.26−31 The interface between domains confines the polymer chains, which must relax through a hindered reptation process or through arm retraction relaxations.26 The terminal response transitions to nonliquid-like scaling in G′(ω) and G′′(ω), which is dependent on the long-range order of the morphology as well as the nature of defects.32 The presence of microphase segregation in the dbBB systems introduces new considerations for structure−property relationships in comparison to the well-studied hBB materials. Recently, the linear viscoelasticity of model poly(styrene)block-poly(ethylene oxide) (PS-b-PEO) dbBBs was characterized over a range of block compositions.14 The rheological properties were compared to that of PS-b-PEO LBCPs with analogous nanostructures. The combination of the brush architecture and microphase separation produced a rheological response clearly distinct from that of the LBCPs. The suppression of an entanglement plateau resulted in liquid-like rheology despite large overall Mw (up to 750 kg/mol). While the liquid-like rheology supported the dbBBs ability to rapidly self-assemble in the melt, a distinct connection between the rheological response and specific morphology (e.g., lamellar, cylindrical, or spherical) was still missing. Here, we study the structure and viscoelasticity of dbBBs with precise control over side chain length (Nsc), block composition (f), and overall backbone length (Nbb), over a range of Mw (up to 500 kg/mol). The dbBBs exclusively assemble into lamellar morphology. The objectives are to determine viscoelastic patterns, to propose possible structural mechanisms responsible for the observed rapid response, and to represent them in a rheological model. Our focus is on the fast ordering dynamics of the dbBBs, which we attribute to internal liquid-like regions, which consist of a high concentration of free chains ends and form internal slip layers (ISL). We further discuss aspects of the molecular asymmetry due to a step change in side chain length (Nsc‑A ≠ Nsc‑B), which is expected to impact the microstructure and the rheological properties. Exploration of this parameter space will expand our understanding of the unique behavior of these emergent materials.

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Figure 1. Schematic representation of dbBB series of increasing total backbone degree of polymerization (Nbb) with constant side chain lengths (PS Mn = 2.9 kg/mol, PEO Mn = 5 kg/mol) and block composition (f PEO ∼ 0.5). Asymmetric molecular shape arises from the difference in PS and PEO side chain length, resulting in blocks with asymmetric backbone degree of polymerizations (Nbb‑PS/Nbb‑PEO ≈ 1.6). resembles a “worm-like” conformation, while on in the PEO block, Nsc‑PEO > Nbb‑PEO and the shape is more “star-like” rather than the conventional “worm”(Table 1). The flexibility of the backbone is described by the persistence length (lp), which scales with Nsc.33 Therefore, the rigidity of the backbone is influenced by the steric crowding of the side chains. A bottlebrush with norbornene-based backbone is thought to be semiflexible, with a lp of about 5 backbone repeat units (∼3.1 nm) according to recent SCFT calculations.10,34 However, the side chain asymmetry influences the unique lp of each block, where the longer PEO side chains should contribute more stiffness to their backbone segment than the PS side chains do to its own backbone (lp‑PEO > lp‑PS). There is also a contrast in the side chain flexibility. The short PS side chains are much stiffer and more sterically hindered than the longer, more flexible PEO side chains. Overall, the dbBBs possess a PS block with a long backbone and short, stiff side chains and a PEO block with a shorter backbone and longer flexible side chains.

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MATERIALS

EXPERIMENTAL METHODS

Sample Preparation. A 5 wt % solution of each dbBB was prepared in anhydrous dichloromethane (DCM) and drop-cast onto glass on a flat stage under a nitrogen atmosphere. After the solvent was evaporated, the dried films were collected. Approximately 30 mg

A series of PS-b-PEO dbBBs with short side chains (PS-NB Mn = 2.9 kg/mol, PEO-NB Mn = 5 kg/mol) were synthesized by sequential ring opening metathesis polymerization (ROMP) of norbornene modified macromonomer side chains according to procedures from previous B


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Macromolecules Table 1. Molecular Characteristics of PS-b-PEO Diblock Bottlebrush Series PS-b-PEO dbBB sample namea

Mw (kg/mol)b

Đb

f PEOc

Nbbd

Nbb‑PSd

Nbb‑PEOd

d0 (nm)e

dbBB-21 dbBB-40 dbBB-55 dbBB-72 dbBB-119

86 160 230 300 560

1.14 1.12 1.11 1.14 1.27

0.51 0.51 0.51 0.51 0.50

21 40 55 72 119

13 25 34 45 74

8 15 21 27 45

29.3 36.9 42.3 65.4 90.0

a dbBBs are labeled as “dbBB-X”, where “X” = total backbone degree of polymerization (Nbb). bWeight average molecular weight (Mw) and polydispersity (Đ) were determined by GPC-MALLS. cTheoretical volume fraction of PEO ( f PEO) was calculated using mass ratios of PS and PEO obtained from 1H NMR spectra and approximate bulk densities (1.05 and 1.09 g/cm3 for PS and PEO, respectively). dBlock backbone degree of polymerizations (Nbb‑PEO and Nbb‑PS) and overall backbone degree of polymerization (Nbb= Nbb‑PEO + Nbb‑PS) were calculated using absolute molecular weights and Đ as measured by GPC and mass fraction from NMR. eDomain spacings (d0) of microphase separated dbBBs were calculated using the equation d-spacing = 2π/q*, where q* corresponds to the primary peak from small angle X-ray scattering in nm−1.

of bulk material was packed into a circular metal mold and sandwiched between pieces of Kapton tape. The samples were annealed under vacuum for 4 h at T = 120 °C and subsequently cooled to room temperature. X-ray Scattering. Microphase separation and domain spacings were characterized by small-angle X-ray scattering (SAXS) using a Ganesha SAXS-LAB instrument with Cu Kα 0.154 nm line on SAXS or USAXS mode. X-ray beam area was 0.04 mm2. In situ temperature controlled SAXS was performed with a Linkam HFS600E-P temperature stage over a temperature range of T = 25−200 °C using increments of approximately 30 K (T = 25, 50, 80, 110, 140, 170, and 200 °C). The heating rate was 10 K/min followed by 5 min of thermal equilibration before each isothermal measurement. Domain spacings d0 = 2π/q* were determined from q*, the primary peak position in nm−1. Electron Microscopy. Cryo-microtoming (Leica Ultracut microtome) was used to cut bulk samples into 50 nm thin films. Sections were collected using a carbon film supported by copper grids. Subsequent ruthenium tetroxide (RuO4) staining improved the contrast between PS and PEO domains. The prepared thin films were imaged by transmission electron microscopy (TEM) on a JEOL 2000FX (200 kV). Rheology. Dynamic moduli were measured using small-amplitude oscillatory shear (SAOS) between ω = 1 and ω = 100 rad/s in a Malvern Kinexus rotational rheometer with an 8 mm parallel plate geometry. Measurements were conducted within the linear viscoelastic regime (LVR) at strain amplitudes of γ = 0.01. SAOS frequency sweeps were obtained over a temperature range from T = 90 to 170 °C at 10 K intervals. The elevated temperatures avoided contributions from PEO crystallization. The time−temperature superposition (tTS) principle was found to apply over the experimental temperature range. Rheological data were analyzed using IRIS Rheo-Hub 2018 software.35

Figure 2. Room temperature 1-D SAXS spectra of dbBBs after thermal annealing for 4 h at 120 °C. Higher order Bragg reflections are identified at a ratio of q*/2q*. Arrows designate scattering peaks from PEO crystal lamellae.

graphs in Figure 3a−e confirm the lamellar morphology. Microtomed slices were stained to provide contrast between the PEO domain (dark) and PS domain (light). The trend of increasing d0 is also observed in the micrographs. The width of the stained PEO domain appears thinner than the PS domain due to the shorter relative Nbb and the star-like conformation. The temperature dependent phase behavior was characterized by in situ temperature controlled SAXS. Preannealed dbBB samples were heated from room temperature to T = 200 °C using temperature steps of 30 K (Figure 4a−e). Microphase separation (indicated by q*) persists up to T = 170 °C (the highest temperature in rheological characterization by SAOS). The high order peak 2q* disappears upon heating through T = 80 °C (above Tm of the PEO crystals), indicating a loss of long-range order in the lamellar packing. The transition appears to be universal across the range of Nbb. While the intensity of q* does decrease (likely due to electron density differences between crystalline and amorphous PEO domains), the full width at half-maximum (fwhm) of q* does not shift substantially (Figure S5). Only the long-range order is impacted such that, in the mobile melt state, the PS and PEO domains are still microphase segregated, but the lamellar packing is macroscopically disordered. At T = 200 °C, a microphase separation transition (MST) to the homogeneous state is ultimately observed, indicated by the complete disappearance of q*.

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RESULTS Self-Assembly and Morphology. The dbBBs selfassembled into ordered lamellae after thermal annealing due to microphase separation between the chemically dissimilar blocks. Primary scattering peaks (q*) appeared in all five samples, as well as high order reflections at peak ratios of q*/ 2q* (Figure 2). The rapid self-assembly is consistent with previous reports of fast ordering dynamics for dbBBs with short side chains.3,5 PEO crystallization was observed at room temperature, especially in the larger Nbb samples, evidenced by a Bragg scattering peak at ∼q = 0.4 nm−1. In some cases, anisotropic 2-D scattering patterns were observed, indicating some alignment of the lamellar domains at room temperature (Figure S3). The lamellar domain spacing d0 (determined from SAXS using the equation d0 = 2π/q*) increases systematically from d0 = 23 to 90 nm with increasing Nbb. The self-assembly at room temperature was also investigated with transmission electron microscopy (TEM). TEM microC


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Figure 3. Transmission electron microscopy (TEM) of cryomicrotomed dbBB samples after thermal annealing. (a) dbBB-21; (b) dbBB-40; (c) dbBB-55; (d) dbBB-72; (e) dbBB-119. Dark domains are stained PEO while bright domains correspond to PS. All scale bars are 100 nm.

Figure 4. Log−log spectra of in situ temperature controlled SAXS for dbBB series from room temperature through 200 °C. (a) dbBB-21; (b) dbBB-40; (c) dbBB-55; (d) dbBB-79; (e) dbBB-119. Scattering intensity normalized by intensity of incident beam and a constant sample thickness (0.5 mm).

The ordered lamellae reform upon cooling back to room temperature (Figure S6). Here, the MST is accessible (TMST > 170 °C), and rapid ordering can be induced upon quenching. The structure transition highlights the potential for processing of these specific materials and suggests many interesting opportunities for flow induced alignment. Linear Viscoelasticity. The linear viscoelasticity of the microphase separated dbBBs was characterized using small amplitude oscillatory shear (SAOS) frequency sweeps from T = 90 to 170 °C. The structure is unchanged across the

temperature range, and the dbBBs are thermorheologically simple so that time−temperature superposition (tTS) can be applied. The origins of thermorheological simplicity in heterogeneous materials seems counterintuitive, in the sense that relaxation processes from multiple components may maintain individual temperature dependence.36 There is no theoretical basis for the determination of shift factors aT in multiphase polymer systems, but if the viscoelastic contrast is high, the contribution of one component will dominate.36,37 The applicability of tTS for PS-b-PEO dbBBs within the D


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structural rearrangements of a material in time.39 G(t) is a monotonically decaying function which is defined as the integral over relaxation modes from 0 < τi < τmax of the relaxation time spectrum H(τ) (eq 1).39

experimental composition range is consistent with previous results that show the onset of tTS failure at f PEO ∼ 0.75, suggesting that the dynamics in the PS domain dominate the thermorheological response in this system.14,38 Master curves of storage and loss modulus (G′(ω), G′′(ω)) at Tref = Tg‑PS + 30 °C are presented in Figure 5a. Horizontal shift factors aT

G (t ) =

∫0

τmax

dτ H (τ )e − t / τ τ

(1)

H(τ) is a continuous function which can be directly calculated from dynamic data, for example, through techniques established by Baumgaertel and Winter.40 Figure 6 shows

Figure 5. (a) Master curves of dynamic moduli G′(ω) (open symbols) and G″(ω) (closed symbols) for PS-b-PEO dbBB samples at a reference temperature of Tref = Tg‑PS + 30 °C. Master curves separated vertically (factor A) to provide clarity: dbBB-21, × 100; dbBB-40, × 101; dbBB-55, × 102; dbBB-72, × 103; dbBB-119, × 104. (b) Normalized storage modulus (G′/G*) versus shifted frequency (aTω) for dbBB series.

can be represented with the WLF equation (Figure S7) and are generally independent of Nbb with slight variability due to the heterogeneous microphase separation. Tref was defined at a set distance from Tg‑PS (determined by DSC in Figure S8) to appropriately compare the time scales of the various relaxation processes. In Figure 5a, G′(ω) and G′′(ω) are vertically separated by an extra factor (A) for clarity. The viscoelastic response is consistent with previous data of PS-b-PEO dbBBs, notably elastically dominated behavior at the highest frequencies (aTω > 104 rad/s), and an intermediate frequency regime of viscously dominated behavior, where G′′(ω) > G′(ω).14 The dbBBs are unentangled, as no distinct plateau in G′(ω) is observed. At lower frequencies (aTω ∼ 101 rad/s), a crossover in viscoelastic character occurs. This relaxation feature begins to shift to lower frequency and becomes more pronounced with increasing Nbb. At the low frequency limit, the dbBBs do not display liquid-like terminal scaling limit of G′(ω) ∼ ω2 and G′′(ω) ∼ ω1 but exhibit power law scaling in G′(ω) and G′′(ω), as well as a slight increase in elasticity. The dynamic data in Figure 5a can be expressed using a variety of additional viscoelastic functions. All show multimodal, sequential relaxation patterns (Figure S9). The normalized storage modulus (G′/G*) in Figure 5b delineates these different features most clearly. Notably, the maxima in G′/ G* shift to lower frequency and are significantly drawn out over a wider frequency range for the longer backbones. The viscoelastic terminal behavior suggests that there are consequences of the microphase separated structure in comparison to the homogeneous hBB melts, which display liquid behavior in the terminal regime.22 Relaxation Time Spectra Analysis. The correlation between structure and dynamics is expanded through additional analysis of the relaxation modes across the wide range of accessible relaxation times. The relaxation modulus G(t) is a powerful parameter when describing the viscoelastic response of a material under all flow conditions, as it expresses the

Figure 6. Continuous relaxation time spectra H(τ) calculated from dynamic data according to Baumgaertel and Winter40 and fit to the general dual power law spectrum (eq 2) shown in black. Fit parameters to the general spectrum are available in Table S2. Fit parameters to individual dbBB samples are in Table 2.

calculated H(τ) for all dbBB. All spectra appear to overlap each other and exhibit a similar decaying power law form. Power law scaling implies the relaxations are “self-similar” or “scale invariant” across a wide time window. Self-similarity is used to describe the extent of structural connectivity or the molecular dynamics that drive the respective modes.41 Distinct scaling regimes govern the spectra across all τ < τmax, much like the sequential relaxations in the dynamic viscoelastic response (Figure S9). The multimodal behavior can be crudely represented by a single power law. Specifically, a dual power law model (eq 2) is used to represent this behavior more closely:

1 2 ij ij τ yz τ yz H(τ ) = H0 + H1jjj1 + zzz + H2jjj1 + zzz j j τ1 z{ τ2 z{ (2) k k where H0, H1, and H2 are constants, τ1 and τ2 are characteristic relaxation times, and n1 and n2 are the relaxation exponents. Typically, ni may adopt a value between 0 and 1, where the extreme limit of ni = 0 is a Hookean solid.39 To represent the experimental data, a cutoff was applied at τmax = 104 s. As a result, H(τ) = 0 for all modes τ > τmax and H0 ∼ 0. Various alternative forms of the dual power law are proposed in the Supporting Information, but eq 2 represents the dbBB response most accurately. A general fit of eq 2 to H(τ) is marked by a solid black line in Figure 6, while individual fits were also made for each spectrum (Figure S10). Fit parameters for the individual samples are presented in Table 2. H(τ) can be used to predict all other dynamic material functions, and the

−n

E

−n


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Macromolecules Table 2. Parameters of Dual Power Law Model (Eq 2) Fit to dbBB Samples PS-b-PEO dbBB sample namea dbBB-21 dbBB-40 dbBB-55 dbBB-72 dbBB-119

H1 (Pa) 1.7 4.0 3.4 4.8 3.4

× × × × ×

106 106 106 106 106

τ1 (s) 4.9 2.9 3.5 4.5 6.4

× × × × ×

n1

10−5 10−5 10−5 10−4 10−4

0.83 0.83 0.82 0.86 0.81

H2 (Pa) 7.5 9.4 9.0 8.3 4.3

× × × × ×

103 103 103 103 103

τ2 (s) 5.4 1.0 1.3 2.0 7.0

× × × × ×

10−1 100 100 100 100

n2 0.68 0.67 0.71 0.67 0.64

dbBBs are labeled as “dbBB-X”, where “X” = total backbone degree of polymerization (Nbb).

a

fit to the experimental dynamic data is remarkably accurate (Figure S11). The linear superposition of two power laws describes behavior on short and long time scales, respectively. Short time modes correspond to relaxations across small scale structural detail. In the first power law regime at the shorter relaxation times, a scaling exponent of n1 ≈ 0.83 is observed, indicating extremely rapid relaxation of stress. In the second regime, the power law scaling increases slightly to n2 ≈ 0.67. The feature is extended to longer relaxation times with increasing Nbb, reflected by the increase in τ2 of over a decade in τ (Table 2). The shift in relaxation time is consistent with the draw out relaxation feature in Figure 5b. Surprisingly, the exhibited scaling behavior is remarkably like a critical gel approaching the liquid-to-solid transition, where the structure is on the brink of a sample spanning connectivity limit.39 The long time modes are attributed to structural rearrangements over the largest structural scale, where the microphase segregation is expected to dominate. Various power law relaxation responses have been identified in analogous layered materials, such as strongly segregated lamellar BCPs and liquid crystal assemblies.26,30,32,41−44 However, here, the morphology data depicts a system with unentangled side chains, asymmetric block design, and a globally disordered morphology in the melt. The emergence of sequential scaling regimes on short and long time scales suggests the possibility of new relaxation mechanisms arising from the dbBB architecture. The conformation of asymmetric dbBBs in the melt state must be discussed to resolve these observed phenomena in a rheological model.

PS) dbBB samples in which both blocks appeared to span the star-to-worm regime.10 The overall trend also holds for asymmetric systems in which only one block is primarily “worm-like” (PS domain) as the star-like PEO domain always remains compact and scaling is not a strong function of Nbb. Asymmetries between the two blocks influence the structuredynamics relationship in the melt state as well as the lamellar assembly at room temperature. The long-range order of the lamellar packing deteriorates in the melt state according to temperature resolved SAXS. A lamellar morphology forms when the minimized interfacial curvature is equal, resulting in a flat interface.1 In linear BCPs, the curvature is equalized when the volume fraction between two diblocks is symmetric. In the dbBBs with asymmetric side chain length, the longer PEO side chains are expected to force curvature at the interface. Even though the two diblocks of the PS-b-PEO dbBBs appear to occupy different geometries on each side of the interface, the necessary curvature is satisfied at room temperature.46 The difference in molecular shape between blocks leads to a competition of both space and volume filling, yet the minimization of side chain stretching and interfacial area is still desired. Recent experiments have suggested that the backbone will adjust to accommodate asymmetric side chain lengths, graft density, and graft distribution to enable the formation of lamellae.11,12,47 Inherent constraints in the system could lead to nonequilibrium structures throughout the domains that likely contribute to macroscopic disordering in the melt.48 At room temperature, the PEO domain is semicrystalline and the PS domain is glassy according to DSC measurements (Figure S8). It is well-known that crystallinity is a strong driving force that can dictate self-assembly and the ordering transition.49−52 The melting of PEO impacts the global ordering of the lamellae but not the local microphase segregation or characteristic spacing. Therefore, the stiff and rigid PEO crystals assists the flat interface and the persistence of long-range lamellar order. A similar phenomenon was recently proposed by Chae et al. in dbBBs with crystallizable POSS pendants groups that supported well-ordered lamellar morphology despite asymmetric molecular shape.53 The reformation of lamellar morphology in the PS-b-PEO dbBBs after cooling back to room temperature is consistent with the hypothesis that the long-range morphology is coupled with the presence of stiff crystallites. While a minor change in the PEO brush bulk density should be expected through the melting transition (ρPEO = 1.12 g/cm3 (crystalline) and 1.09 g/cm3 (melt)), it does not appear to significantly impact d0.54 Crystallization of densely grafted bottlebrush macromolecules and their coassembly within BCPs certainly requires additional investigations. Regardless, PEO crystallization and long-range lamellar order do not appear to impact the rheological properties characterized in the melt state for this set of dbBBs.

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DISCUSSION Asymmetric Diblocks. The brush architecture introduces new considerations for molecular arrangement and dynamics due to the dense side chain grafting. In dbBBs, contrasting side chain design adds another dimension to the unique physical properties. The molecular shape of each block was described as “star-like” and “worm-like” for PEO and PS, respectively. In the star conformation, Nsc and Nbb are commensurate. The brush block begins to adopt the conventional worm-like conformation as Nbb becomes larger than Nsc.10 The extended backbone of the worm-like conformation is quantified through the scaling relationship between the domain spacing and total backbone degree of polymerization (do ∼ Nbbα).5,10,12,13 The scaling exponent for symmetric linear BCPs with coil-like conformation is α = 0.66 in the strong segregation limit.45 Overall, the scaling for the PS-b-PEO dbBBs depicts an extended backbone conformation resulting in an exponent α = 0.84 (Figure S4). However, the scaling exponent decreases significantly (α = 0.36) at the low Nbb limit where do becomes much more dependent on Nsc rather than Nbb. The relationship between do and Nbb is in close agreement with symmetric atactic poly(propylene)-block-poly(styrene) (aPP-bF


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Figure 7. Schematic representation of asymmetrically shaped PS-b-PEO dbBBs locally assembled into a microphase separated layer. Backbone blocks rapidly slide along each other, producing internal slip layer (ISL) relaxations within each domain (dotted arrows). The side chains themselves avoid overlap due to steric crowding and repulsive forces. The domain interface (dashed line) is set at the junction point between PEO and PS blocks, further constraining side chains.

is resolved by the first relaxation exponent n1 and dominates the power law across the time window. As previously mentioned, n1 ≈ 0.83 is extremely rapid, much faster than that predicted for Rouse (n = 0.5) or Zimm (n = 0.66) modes.41 Here, the scale invariant relaxation is likely a measure of the molecular dynamics rather than self-similarity in the connectivity or structural arrangement. The wide window of such rapidly relaxing power law scaling (over three decades of τ) is not observed in the hBB materials with short side chains. For example, H(τ) was calculated from dynamic data of densely grafted poly(lactide) (PLA) hBBs with short side chains from Haugan et al. (Figure S13).21 Dynamically, hBBs look very similar to critical gels but only show one power law exponent of n ≈ 0.6 across experimental time scales. At the longest accessible times (τ ∼ τmax), the spectrum deviates to the viscoelastic liquid limit.39 The relaxation of the semiflexible PLA chains is not characteristic of the rapid confined ISL process described by n1. The conventional relaxation of the dbBBs is restricted by the interface, which is consistent with the segregation of the two blocks into their own distinct liquid layers. The PEO and PS layers relax cooperatively in this regime but likely exhibit different relaxation dynamics due to the asymmetric molecular configurations and difference in segmental friction. Although the semiflexible backbones have sufficient mobility to slip in both domains, the cooperative relaxation is likely dominated by the more worm-like PS dynamics. Convolution within the spectrum could contribute to the deviations in the transition at τ ∼ 10−4 s, which is broader at low Nbb. As Nbb increases, the scaling of n1 forms a sharper, more distinct power law regime as the architecture transitions to a more typical worm-like configuration. In the second regime, scaling of n2 is governed by the largest structure that can relax, which is now the interdomain structure (i.e., the microphase separated morphology). Scaling of n2 ≈ 0.67 is slower and softer than the relaxations in n1 but still remarkably like a critical gel near the liquid-to-solid transition. According to SAXS, the lamellae are macroscopically disordered, are weakly correlated over large length scales, and likely possess many defects. Composition fluctuations are large enough to produce significant q* with static characteristic length in SAXS, but the equilibrium structure fluctuates in time due to the high molecular mobility of the ISL within the

Sequential Relaxations of Microphase Separated Bottlebrushes. The rheology of the melt state is governed by several structural details across the microphase separation, macromolecular architecture, and side chain chemistries. As such, multiple relaxation mechanisms contribute to the total response. The segmental relaxations of the side chains (the smallest structural length scale) are resolved on the shortest accessible time scales in the high ω regime, where the dynamics are elastically dominated.19,22 The power law scaling of the complex modulus η*(ω) ∼ ω−0.7 (Figure S12) is compared to that of aPP hBBs with short side chains which scale at η*(ω) ∼ ω−1 in the segmental/glassy regime.19 The PS-b-PEO dbBBs do not approach the extreme scaling limit due to the presence of microphase separation. In a two-phase morphology, the glassy characteristics of each domain are individually expressed and convolute the response. Here, the structure is analogous to hard glassy plates (PS domain) separated by a melted amorphous layer (PEO domain). Both the glassy PS and the amorphous PEO domains lead to a “reduced” glassy response on the shortest time scales. The PS domain Tg are all below that expected for bulk PS (Tg ∼ 100 °C) according to DSC. The Tg is broad and appears to increase slightly with Nbb, contrasting observations in the hBB materials, where Tg is independent of Nbb and more closely a function of Nsc.19,22 It is possible that the star-like architecture at low Nbb additionally suppresses Tg in the PS domain.55 The transition of H(τ) into the first power law regime (τ ∼ 10−4 s) represents a shift away from the fast relaxations dominated by segmental side chains. The subsequent structural detail now spans the microphase separated domain. Here, side chains are unentangled and fully relaxed. Steric repulsions between neighboring side chains along the backbone force the block to extend into the center of the domain, away from the interface. The interpenetration of side chains from neighboring blocks is reduced in the densely grafted bottlebrush system.33 The blocks may appear constrained schematically, but the intradomain structure is essentially a confined liquid melt. Side chains connected to the end of each block, far from the interface, form a layer of free chain ends in the center of the domain. The absence of chain entanglements allows the blocks to freely slide along each other, resulting in an internal slip layer (ISL) (Figure 7). The intradomain relaxation of the ISL G


Article

Macromolecules segregated domains.56 The power law behavior at the longest time scales is reminiscent of that found in symmetric LBCPs quenched into the ordered state, where scaling of G′(ω) ∼ G′′(ω) ∼ ω0.5 at low ω is described by both experiments and theory.43,57 Here, the terminal relaxation time is pushed to longer time scales due to the cooperative motion of the structural pattern and additional fluctuation effects at the interface. In comparison, the relaxations in fully disordered LBCP melts resemble that of a liquid.44 The critical gel behavior is clearly a function of the structure but not directly through a “self-similar” feature across the structural length scales.41 The dbBBs show critical gel-like relaxations despite the rather disordered structural pattern in the melt. We propose that persistence of critical gel behavior and the difference from the predicted value of n = 0.5 is due to the interface between the diblocks, which is preserved well into the melt state. There is a large compositional difference across the interface due to the larger specific interfacial area and strong segregation in the brush architecture. For those side chains close to the interface, thermodynamic driving forces induce significant repulsion of side chains contributing to the backbone stretching and elongation.10 Side chains along the backbone further away from the interface show increased degrees of freedom and orientation compared to the confined arrangement at the interface and contribute to the high mobility of the chain ends in the ISL. The diblocks are confined perpendicularly to the interface but have mobility to rearrange within the interface itself. 31 The additional rearrangement mechanism within the interface is facilitated by the reduced interpenetration of side chains from neighboring blocks. On the longer time scales, the interfacial relaxation is convoluted with the cooperative relaxation of the microstructure. In many respects, the schematic picture of semiflexible, unentangled macromolecules penetrating perpendicularly from a segregated interface is similar to surfactants at a liquid interface or with the layered liquid super structure of self-assembled liquid crystals described by Larson et al., where power law scaling at low ω limit is indistinguishable from macroscopically disordered lamellar poly(styrene)-block-poly(isoprene).26 The emergence of critical gel behavior in the dbBBs suggests the phase transition into the melt state is fundamentally different from the case of ideal symmetric LBCPs. A comprehensive understanding of the thermodynamic order-to-disorder transition (ODT) in densely grafted brush systems is still an open question and the subject of future investigations. In the case of the dbBB, the sequential scaling regimes on short and long time scales arises from the microphase separation of the two densely grafted diblocks. The magnitude of the scaling exponents implies extremely rapid relaxation processes and high molecular mobility. While sequential “dual” relaxation behavior has been identified in the hBB materials, those dual relaxations develop from an entirely different mechanism. Normally, the worm-like chains relax through a single scale invariant mode before the terminal relaxations. A second plateau in G′ emerges only when Nsc is large and the side chains become entangled, resulting in two sequential relaxation features.22,25 In the dbBB systems considered, Nsc is kept well below entanglement. Therefore, the interface between the diblocks plays a crucial role in restricting the normal Rouse-like or reptation modes of the brushes, which gives rise to the two new relaxation mechanisms.

The dbBBs are unentangled over an exceptionally wide range of Nbb, corresponding to significantly large d0 relevant for optical and metamaterial applications.3,15 The combination of rheological properties akin to low Mw, unentangled systems with the nanostructure of high Mw, entangled systems is remarkable. Additionally, the dual power law model for H(τ) represents the relaxations modes exceptionally well. The model could be further implemented to compare structure−property relationships in analogous materials that display similar critical gel-like behavior or sequential relaxation processes. For example, the dual model will help quantitatively differentiate the relaxation processes in hBB systems with long entangled side chains. The rheological properties and relaxation processes in dbBBs with symmetric block design are not well-defined in the literature, nor are systems with strong long-range order in the melt state (lamellar, cylindrical, or spherical morphology). Analysis of H(τ) and quantification of the relaxation processes in such systems will certainly improve our understanding of the structure−property relationships in these emergent materials.

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CONCLUSION A series of PS-b-PEO bottlebrush diblock copolymers were synthesized using sequential ROMP over a wide range of backbone degree of polymerizations Nbb. The reduced entanglements resulting from short side chains enable rapid self-assembly into lamellar structures. A microphase separated, macroscopically disordered morphology persisted across the experimental temperature range of the rheological characterization. The bottlebrush architecture governs the rheology across the range of Nbb. Specifically, the high frequency regime was elastically dominated, resulting from the glassy response of segmental side chains. Otherwise, most relaxation processes are dominated by two relaxation modes represented by a new dual power law model for the relaxation time spectrum H(τ) (eq 2). The PS-b-PEO dbBBs in the series exhibit scaling exponents of n1 ≈ 0.83 and n2 ≈ 0.67, typical for critical gels. The faster mode (n1) is attributed to intradomain dynamics, where unentangled side chains and semiflexible backbones freely “slide” along each other through an internal slip layer (ISL) relaxation process. The ISL is facilitated by a liquid region of free chain ends in the center of the layer. The ISL phenomenon appears to be unique for the layered dbBBs. The second power law mode (n2) is attributed to the global morphology and the interface, which is still relatively soft and requires longer times to relax stress. The dual power law model for H(τ) captures each sequential process in the viscoelastic response of the dbBBs and is applied to compare the unique relaxation behavior to other densely grafted hBB systems and comparable layered materials.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01843. Additional characterization details, description of architectural length scales, and dual power law model details; 1H NMR and GPC traces of PS-NB and PEONB macromonomers and PS-b-PEO bottlebrush copolymers; 2D SAXS patterns of materials after thermal annealing; scaling relationship between domain spacing H


Article

Macromolecules

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(13) Hong, S. W.; Gu, W.; Huh, J.; Sveinbjornsson, B. R.; Jeong, G.; Grubbs, R. H.; Russell, T. P. On the Self-Assembly of Brush Block Copolymers in Thin Films. ACS Nano 2013, 7 (11), 9684−9692. (14) Yavitt, B. M.; Gai, Y.; Song, D.-P.; Winter, H. H.; Watkins, J. J. High Molecular Mobility and Viscoelasticity of Microphase-Separated Bottlebrush Diblock Copolymer Melts. Macromolecules 2017, 50 (1), 396−405. (15) Liberman-Martin, A. L.; Chu, C. K.; Grubbs, R. H. Application of Bottlebrush Block Copolymers as Photonic Crystals. Macromol. Rapid Commun. 2017, 38, 1700058. (16) Song, D.-P.; Shahin, S.; Xie, W.; Mehravar, S.; Liu, X.; Li, C.; Norwood, R. A.; Lee, J.-H.; Watkins, J. J. Directed Assembly of Quantum Dots Using Brush Block Copolymers for Well-Ordered Nonlinear Optical Nanocomposites. Macromolecules 2016, 49 (14), 5068−5075. (17) Song, D.-P.; Jacucci, G.; Dundar, F.; Naik, A.; Fei, H.-F.; Vignolini, S.; Watkins, J. J. Photonic Resins: Designing Optical Appearance via Block Copolymer Self-Assembly. Macromolecules 2018, 51 (6), 2395−2400. (18) Altay, E.; Nykypanchuk, D.; Rzayev, J. Mesoporous Polymer Frameworks from End-Reactive Bottlebrush Copolymers. ACS Nano 2017, 11 (8), 8207−8214. (19) López-Barrón, C. R.; Brant, P.; Eberle, A. P. R.; Crowther, D. J. Linear Rheology and Structure of Molecular Bottlebrushes with Short Side Chains. J. Rheol. (Melville, NY, U. S.) 2015, 59 (3), 865−883. (20) Namba, S. I.; Tsukahara, Y.; Kaeriyama, K.; Okamoto, K.; Takahashi, M. Bulk Properties of Multibranched Polystyrenes from Polystyrene Macromonomers: Rheological Behavior I. Polymer 2000, 41, 5165−5171. (21) Haugan, I. N.; Maher, M. J.; Chang, A. B.; Lin, T.-P.; Grubbs, R. H.; Hillmyer, M. A.; Bates, F. S. Consequences of Grafting Density on the Linear Viscoelastic Behavior of Graft Polymers. ACS Macro Lett. 2018, 7, 525−530. (22) Dalsin, S. J.; Hillmyer, M. A.; Bates, F. S. Linear Rheology of Polyolefin-Based Bottlebrush Polymers. Macromolecules 2015, 48, 4680−4691. (23) Dalsin, S. J.; Hillmyer, M. A.; Bates, F. S. Molecular Weight Dependence of Zero-Shear Viscosity in Atactic Polypropylene Bottlebrush Polymers. ACS Macro Lett. 2014, 3 (5), 423−427. (24) Tsukahara, Y.; Namba, S. I.; Iwasa, J.; Nakano, Y.; Kaeriyama, K.; Takahashi, M. Bulk Properties of Poly(Macromonomer)s of Increased Backbone and Branch Lengths. Macromolecules 2001, 34 (8), 2624−2629. (25) Hu, M.; Xia, Y.; McKenna, G. B.; Kornfield, J. A.; Grubbs, R. H. Linear Rheological Response of a Series of Densely Branched Brush Polymers. Macromolecules 2011, 44 (17), 6935−6943. (26) Larson, R. G.; Winey, K. I.; Patel, S. S.; Watanabe, H.; Bruinsma, R. The Rheology of Layered Liquids: Lamellar Block Copolymers and Smectic Liquid Crystals. Rheol. Acta 1993, 32, 245− 253. (27) Bates, F. S. Block Copolymers near the Microphase Separation Transition. 2. Linear Dynamic Mechanical Properties. Macromolecules 1984, 17 (12), 2607−2613. (28) Winey, K. I.; Patel, S. S.; Larson, R. G.; Watanabe, H. Interdependence of Shear Deformations and Block Copolymer Morphology. Macromolecules 1993, 26, 2542−2549. (29) Koppi, K. A.; Tirrell, M.; Bates, F. S.; Almdal, K.; Colby, R. H. Lamellae Orientation in Dynamically Sheared Diblock Copolymer Melts. J. Phys. II 1992, 2, 1941−1959. (30) Rubinstein, M.; Obukhov, S. P. Power-Law-Like Stress Relaxation of Block Copolymers: Disentanglement Regimes. Macromolecules 1993, 26 (7), 1740−1750. (31) Zhang, Y.; Wiesner, U. B. Rheology of Lamellar PolystyreneBlock - Polyisoprene Diblock Copolymers. Macromol. Chem. Phys. 1998, 199, 1771−1784. (32) Colby, R. H. Block Copolymer Dynamics. Curr. Opin. Colloid Interface Sci. 1996, 1, 454−465.

and degree of polymerization; additional viscoelastic functions; DSC of block copolymers (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Benjamin M. Yavitt: 0000-0001-9308-7472 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the NSF Center for Hierarchical Manufacturing at the University of Massachusetts, Amherst (CMMI-1025020). The Department of Polymer Science and Engineering at University of Massachusetts Amherst supported facilities used in this work. We thank Dr. Alice Chang, Dr. Adam Burns, and Dr. Daniel Sunday for helpful discussions of the melt self-assembly of brush block copolymers.

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REFERENCES

(1) Bates, F. S.; Fredrickson, G. H. Block CopolymersDesigner Soft Materials. Phys. Today 1999, 52 (2), 32. (2) Bates, C. M.; Bates, F. S. 50th Anniversary Perspective: Block PolymersPure Potential. Macromolecules 2017, 50 (1), 3−22. (3) Song, D.-P.; Li, C.; Colella, N. S.; Xie, W.; Li, S.; Lu, X.; Gido, S. P.; Lee, J.-H.; Watkins, J. J. Large-Volume Self-Organization of Polymer/Nanoparticle Hybrids with Millimeter-Scale Grain Sizes Using Brush Block Copolymers. J. Am. Chem. Soc. 2015, 137, 12510− 12513. (4) Verduzco, R.; Li, X.; Pesek, S. L.; Stein, G. E. Structure, Function, Self-Assembly, and Applications of Bottlebrush Copolymers. Chem. Soc. Rev. 2015, 44, 2405−2420. (5) Gu, W.; Huh, J.; Hong, S. W.; Sveinbjornsson, B. R.; Park, C.; Grubbs, R. H.; Russell, T. P. Self-Assembly of Symmetric Brush Diblock Copolymers. ACS Nano 2013, 7 (3), 2551−2558. (6) Sveinbjornsson, B. R.; Weitekamp, R. a.; Miyake, G. M.; Xia, Y.; Atwater, H. a.; Grubbs, R. H. Rapid Self-Assembly of Brush Block Copolymers to Photonic Crystals. Proc. Natl. Acad. Sci. U. S. A. 2012, 109 (36), 14332−14336. (7) Song, D.-P.; Lin, Y.; Gai, Y.; Colella, N. S.; Li, C.; Liu, X.-H.; Gido, S. P.; Watkins, J. J. Controlled Supramolecular Self-Assembly of Large Nanoparticles in Amphiphilic Brush Block Copolymers. J. Am. Chem. Soc. 2015, 137 (11), 3771−3774. (8) Xia, Y.; Olsen, B. D.; Kornfield, J. A.; Grubbs, R. H. Efficient Synthesis of Narrowly Dispersed Brush Copolymers and Study of Their Assemblies: The Importance of Side Chain Arrangement. J. Am. Chem. Soc. 2009, 131 (51), 18525−18532. (9) Xia, Y.; Kornfield, J. A.; Grubbs, R. H. Efficient Synthesis of Narrowly Dispersed Brush Polymers via Living Ring-Opening Metathesis Polymerization of Macromonomers. Macromolecules 2009, 42 (11), 3761−3766. (10) Dalsin, S. J.; Rions-maehren, T. G.; Beam, M. D.; Bates, F. S.; Hillmyer, M. A.; Matsen, M. W. Bottlebrush Block Polymers: Quantitative Theory and Experiments. ACS Nano 2015, 9 (12), 12233−12245. (11) Rzayev, J. Synthesis of Polystyrene-Polylactide Bottlebrush Block Copolymers and Their Melt Self-Assembly into Large Domain Nanostructures. Macromolecules 2009, 42 (6), 2135−2141. (12) Lin, T.-P.; Chang, A. B.; Luo, S.-X.; Chen, H.-Y.; Lee, B.; Grubbs, R. H. Effects of Grafting Density on Block Polymer SelfAssembly: From Linear to Bottlebrush. ACS Nano 2017, 11 (11), 11632−11641. I


Article

Macromolecules (33) Paturej, J.; Sheiko, S. S.; Panyukov, S.; Rubinstein, M. Molecular Structure of Bottlebrush Polymers in Melts. Sci. Adv. 2016, 2 (11), No. e1601478. (34) Chang, A. B.; Bates, C. M.; Lee, B.; Garland, C. M.; Jones, S. C.; Spencer, R. K. W.; Matsen, M. W.; Grubbs, R. H. Manipulating the ABCs of Self-Assembly via Low-X Block Polymer Design. Proc. Natl. Acad. Sci. U. S. A. 2017, 114 (25), 6462−6467. (35) Winter, H. H.; Mours, M. The Cyber Infrastructure Initiative for Rheology. Rheol. Acta 2006, 45 (4), 331−338. (36) van Gurp, M.; Palmen, J. Time-Temperature Superposition for Polymeric Blends. Rheol. Bull. 1998, 67, 5−8. (37) Han, C. D.; Kim, J. K. On the Use of Time-Temperature Superposition in Multicomponent/Multiphase Polymer Systems. Polymer 1993, 34 (12), 2533−2539. (38) Bates, C. M.; Chang, A. B.; Momcilovic, N.; Jones, S. C.; Grubbs, R. H. ABA Triblock Brush Polymers: Synthesis, SelfAssembly, Conductivity, and Rheological Properties. Macromolecules 2015, 48 (14), 4967−4973. (39) Winter, H. H.; Mours, M. Rheology of Polymers near LiquidSolid Transitions. Adv. Polym. Sci. 1997, 134, 165−234. (40) Baumgaertel, M.; Winter, H. H. Interrelation Between Continuous and Discrete Relaxation Time Spectra. J. Non-Newtonian Fluid Mech. 1992, 44, 15−36. (41) Winter, H. H. The Occurance of Self Similar Relaxation in Polymers. J. Non-Cryst. Solids 1994, 172-174, 1158−1167. (42) Witten, T. A.; Leibler, L.; Pincus, P. A. Stress Relaxation in the Lamellar Copolymer Mesophase. Macromolecules 1990, 23 (3), 824− 829. (43) Kawasaki, K.; Onuki, A. Dynamics and Rheology of Diblock Copolymers Quenched into Microphase-Separated States. Phys. Rev. A: At., Mol., Opt. Phys. 1990, 42 (6), 3664−3666. (44) Fredrickson, G. H.; Bates, F. S. Dynamics of Block Copolymers: Theory and Experiment. Annu. Rev. Mater. Sci. 1996, 26 (1), 501−550. (45) Semenov, A. N. Contribution to the Theory of Microphase Layering in Block-Copolymer Melts. Zh. Eksp. Teor. Fiz 1985, 88 (4), 1242−1256. (46) Gai, Y.; Song, D.-P.; Yavitt, B. M.; Watkins, J. J. PolystyreneBlock -Poly(Ethylene Oxide) Bottlebrush Block Copolymer Morphology Transitions: Influence of Side Chain Length and Volume Fraction. Macromolecules 2017, 50, 1503−1511. (47) Lin, T.-P.; Chang, A. B.; Chen, H.-Y.; Liberman-Martin, A. L.; Bates, C. M.; Voegtle, M. J.; Bauer, C. A.; Grubbs, R. H. Control of Grafting Density and Distribution in Graft Polymers by Living RingOpening Metathesis Copolymerization. J. Am. Chem. Soc. 2017, 139, 3896−3903. (48) Chang, A. B.; Lin, T.-P.; Thompson, N. B.; Luo, S.-X.; Liberman-Martin, A. L.; Chen, H.-Y.; Lee, B.; Grubbs, R. H. Design, Synthesis, and Self-Assembly of Polymers with Tailored Graft Distributions. J. Am. Chem. Soc. 2017, 139 (48), 17683−17693. (49) Huang, P.; Zhu, L.; Guo, Y.; Ge, Q.; Jing, A. J.; Chen, W. Y.; Quirk, R. P.; Cheng, S. Z. D.; Thomas, E. L.; Lotz, B.; et al. Confinement Size Effect on Crystal Orientation Changes of Poly(Ethylene Oxide) Blocks in Poly(Ethylene Oxide)- b -Polystyrene Diblock Copolymers. Macromolecules 2004, 37 (10), 3689− 3698. (50) Loo, Y. L.; Register, R. A.; Ryan, A. J. Modes of Crystallization in Block Copolymer Microdomains: Breakout, Templated, and Confined. Macromolecules 2002, 35 (6), 2365−2374. (51) Quiram, D. J.; Register, R. A.; Marchand, G. R. Crystallization of Asymmetric Diblock Copolymers from Microphase-Separated Melts. Macromolecules 1997, 30 (16), 4551−4558. (52) Ryan, A. J.; Hamley, I. W.; Bras, W.; Bates, F. S. Structure Development in Semicrystalline Diblock Copolymers Crystallizing from the Ordered Melt. Macromolecules 1995, 28 (11), 3860−3868. (53) Chae, C.; Yu, Y.; Seo, H.; Kim, M.; Grubbs, R. H.; Lee, J. Experimental Formulation of Photonic Crystal Properties for Hierarchically Self-Assembled POSS − Bottlebrush Block Copolymers. Macromolecules 2018, 51 (9), 3458−3466.

(54) Zhu, L.; Cheng, S. Z. D.; Calhoun, B. H.; Ge, Q.; Quirk, R. P.; Thomas, E. L.; Hsiao, B. S.; Yeh, F.; Lotz, B. Phase Structures and Morphologies Determined by Self-Organization, Vitrification, and Crystallization: Confined Crystallization in an Ordered Lamellar Phase of PEO-b-PS Diblock Copolymer. Polymer 2001, 42, 5829− 5839. (55) Ren, J. M.; McKenzie, T. G.; Fu, Q.; Wong, E. H. H.; Xu, J.; An, Z.; Shanmugam, S.; Davis, T. P.; Boyer, C.; Qiao, G. G. Star Polymers. Chem. Rev. 2016, 116 (12), 6743−6836. (56) Bates, F. S.; Rosedale, J. H.; Fredrickson, G. H. Fluctuation Effects in a Symmetric Diblock Copolymer near the Order − Disorder Transition. J. Chem. Phys. 1990, 92 (1990), 6255. (57) Rosedale, J. H.; Bates, F. S. Rheology of Ordered and Disordered Symmetric Poly(Ethylenepropylene)-Poly(Ethylethylene) Diblock Copolymers. Macromolecules 1990, 23 (8), 2329−2338.

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Power Law Relaxations in Lamellae Forming Brush Block Copolymers

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