Linear Rheology of Polyolefin-Based Bottlebrush Polymers

Article pubs.acs.org/Macromolecules

Linear Rheology of Polyolefin-Based Bottlebrush Polymers Samuel J. Dalsin,† Marc A. Hillmyer,‡ and Frank S. Bates*,† †

Department of Chemical Engineering and Materials Science and ‡Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455-0421, United States S Supporting Information *

ABSTRACT: Two series of polyolefin-based bottlebrush polymers were synthesized using ring-opening metathesis polymerization of norbornenyl-functionalized macromonomers to compare the rheology of systems with and without the presence of side chain entanglement. The first series of bottlebrushes includes atactic polypropylene (aPP) branches with a fixed length of Mbranch = 2.05 kg/mol and variable backbone degree of polymerization ranging from 11 to 732 (Mw = 22−1500 kg/mol). The branches in this series are shorter than the entanglement molecular weight of aPP (Mbranch/Me ≈ 0.5). The second series utilizes poly(ethylene-alt-propylene) (PEP) branches with Mbranch = 6.7 kg/mol and variable backbone degree of polymerization ranging from 13 to 627 (Mw = 89−4200 kg/mol). The branches in this series exceed the entanglement molecular weight of PEP (Mbranch/Me ≈ 3.5). The linear viscoelastic responses of each sample were examined using smallamplitude oscillatory shear measurements, and dynamic master curves were constructed by time−temperature superposition. Master curves of all aPP bottlebrush polymers exhibited relaxation spectra devoid of any entanglement plateau, despite their high molecular weight. Master curves of the PEP bottlebrushes displayed rubbery plateau regions at short relaxation times, indicating successful entanglement formation between PEP branches. The scaling behavior of the master curves reveals a transient power law scaling throughout the relaxation process. The dynamics are more Zimm-like at early relaxation times and become increasingly Rouse-like at long relaxation times. This transition arises due to the changing conformational character of bottlebrushes at different length scales. Finally, plots of the phase angle versus complex modulus revealed additional intrinsic characteristics of the bottlebrush polymers: (i) the presence of two distinct relaxation processes corresponding to the motion of side chains and of the backbone and (ii) the onset of thermorheological complexity as the glass transition temperature was approached. These two observations represent inherent material properties that are individually governed by the macromolecular architecture and by the monomer scale chemistry, respectively.

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INTRODUCTION The rheological properties of polymeric materials are governed by structure at the molecular level. By adjusting structural details such as stereoregularity, molar mass, or chain architecture, the bulk viscoelastic behavior can be dramatically altered. Polyolefins such as polyethylene (PE) and polypropylene (PP) are known to exhibit shear and extensional rheological responses that are particularly dependent on the degree of branching.1 Long-chain branched polyolefins display improved elasticity and melt strength compared to their linear analogues, and the elongational properties of linear polyolefins can be tuned by blending in a desired amount of long-chain branched polymers.2−5 The linear viscoelastic properties of branched polymer melts have been studied in depth over the past few decades, both experimentally and by theoretical modeling. Several branched polymer architectures have been considered including stars,6−12 combs,13−21 H-polymers,22 and pom-poms.23 The dynamics of these systems are commonly described by a hierarchical relaxation process, in which the outermost branch segments relax first while the internal segments near branch points relax at later times within a solvated tube.24−26 Thus far, less © XXXX American Chemical Society

theoretical consideration has been given to the behavior of bottlebrush polymers in the melt. Bottlebrush polymers are comb-like molecules with a very high density of branches, usually incorporating one or more grafted side chains on every backbone repeat unit. These materials have become an active research area due to advancements in controlled polymerization techniques that enable facile synthesis of polymers with well-defined molecular dimensions.27−29 Specifically, ring-opening metathesis polymerization (ROMP) of macromonomers has proven to be an effective method for bottlebrush synthesis.30−32 Polymerization of macromonomers ensures complete grafting efficiency and regular branch spacing and enables detailed characterization of the branches prior to ROMP. We have employed this technique to synthesize bottlebrush polymers with polyolefin side chains and a poly(norbornene) backbone. Small-amplitude oscillatory shear measurements were then used to explore the influence of Received: May 28, 2015 Revised: June 18, 2015

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DOI: 10.1021/acs.macromol.5b01153 Macromolecules XXXX, XXX, XXX−XXX

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RESULTS AND DISCUSSION Two series of bottlebrush polymers with constant side chain length and variable backbone length were synthesized by ringopening metathesis polymerization (ROMP) of norborneneterminated macromonomers using a third-generation Grubbs catalyst ((H2IMes)(3-BrPy)2(Cl)2RuCHPh; G3) as shown in Figure 1. The first series was produced from atactic

molecular sizes (i.e., brush length and radius) on the resulting rheological behavior. Prior experimental studies have found that the linear viscoelastic responses of bottlebrush polymer melts are controlled by contributions from two different relaxation modes, viz. the characteristic relaxation modes of the side chains and of the entire brush molecules.33−36 This results in dynamic master curves with distinctive features at wellseparated time scales. The first investigation to explore how systematic variation of side chain and backbone lengths affect the rheology of bottlebrush polymers was conducted by Hu et al.34 This study examined nine poly(norbornene)-g-poly(lactide) brush samples with backbone degree of polymerization of 200, 400, and 800, and side chains of Mn/Me = 0.2, 0.5, and 1.0 (where the entanglement spacing, Me, of linear polylactide in the melt is 8.7 kg/mol). Dynamic master curves showed arm relaxation regimes that became more prominent with increasing side chain length. In particular, the samples with the longest side chains (Mn/Me = 1.0) began to display plateaus in the arm regime. However, the relaxation dynamics were interpreted as predominantly Rouse-like for each of the brush samples, and an absence of entanglements was confirmed by analysis of retardation spectra. López-Barrón et al. more recently explored the rheology of bottlebrushes with very short side chains (composed of only 3−6 aPP repeat units) and studied the effects of increasing side chain length on parameters such as Kuhn length, melt viscosity, monomeric friction coefficient, and glass transition temperature (Tg).37 Master curves of these molecules did not show independent side chain and backbone relaxation modes due to the small size of the aPP branches. A primary goal of this work is to examine the effects of side chain and backbone length on the linear rheological behavior, particularly in the limit where side chains will entangle, a limit not yet explored in the literature to the best of our knowledge. How entanglements develop among side chains as the branch molecular weight is increased beyond the entanglement molecular weight (Me) for the corresponding linear chains or whether the crowded arrangement of branches along the backbone chains prevents significant entanglement is an open question. Another aim of this study is to carefully analyze the dynamic moduli data and obtain quantitative scaling information to provide a more extensive understanding of the Rouse-like dynamics. The first series of bottlebrushes in this work includes aPP side chains well below the entanglement molar mass of linear aPP (Mn/Me ≈ 0.5), while the second series contains PEP side chains above the Me of linear PEP (Mn/Me ≈ 3.5). The complex viscosity data for the aPP series were presented in a separate report, which highlighted the dependence of zero-shear viscosity on average molecular weight.38 We now present the full relaxation spectra for this series and compare the results directly with the related PEP bottlebrushes with much longer side chains. The dynamic moduli for each of the bottlebrush samples are first discussed, and the salient features of the master curves are compared. We then examine the power-law scaling behavior of complex viscosity versus frequency and compare the results with predictions of the Rouse and Zimm models. Finally, van Gurp−Palmen analysis is used to characterize the sequential relaxation processes and the apparent thermorheological complexities that arise at low temperatures.

Figure 1. Bottlebrush polymer synthesis by ROMP of macromonomers using a third-generation Grubbs catalyst. Bottlebrushes with aPP and PEP side chains were synthesized by homopolymerization of aPP-NB and PEP-NB macromonomers, respectively.

polypropylene macromonomers (aPP-NB) of Mn = 2.05 kg/ mol, which were synthesized by end-functionalization of a vinyl-terminated aPP precursor using a previously reported protocol.38 The second series was prepared using poly(ethylene-alt-propylene) macromonomers (PEP-NB) of Mn = 6.7 kg/mol. PEP-NB macromonomers were produced by endfunctionalization of hydroxyl-terminated PEP (PEP-OH), which was initially prepared by heterogeneous hydrogenation of anionically polymerized ω-hydroxylpolyisoprene (93% 1,4 addition by 1H NMR) according to well-known procedures.39 Reactions using G3 progressed very rapidly, often complete in less than 5 min, and resulted in bottlebrush products with wellcontrolled molar mass and low dispersity. Linear Rheology of aPP Bottlebrushes. Five bottlebrush samples with aPP side chains and varying backbone lengths were synthesized from aPP-NB (referred to hereafter as poly(aPP-NB)s), and the bulk rheological properties were investigated. The molar mass of each poly(aPP-NB) was controlled by adjusting the catalyst loading, yielding samples with backbone degree of polymerization (DP) ranging from 11 to 732. Characterization of each poly(aPP-NB) is given in Table 1, along with details of the aPP-NB macromonomer and a linear aPP control sample. The results of several preliminary trial polymerizations indicated that a significant decrease in the polymerization rate and an increase in the product dispersity occurred at catalyst loadings less than [aPP-NB]:[G3] = 250. Correspondingly, the polymerizations in Table 1 with higher catalyst loadings were completed in less than 10 min and resulted in narrow molar mass distributions. The increased dispersity at low catalyst B


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Macromolecules Table 1. Molecular and Thermal Characterization of aPP Samplesa sampleb aPP-NB poly(aPP-NB)_11 poly(aPP-NB)_26 poly(aPP-NB)_74 poly(aPP-NB)_215 poly(aPP-NB)_732 aPP_Linearh

[aPP-NB]:[G3]c 10 20 65 150 485

time (min)

convd (%)

10 10 10 10 220

97 97 97 97 94

Mwd (kg/mol) 3.38 22.5 53.1 152 440 1500 203

e

Đd

DPf

Tgg (°C)

1.65 1.07 1.03 1.03 1.12 1.69 1.57

11 26 74 215 732

−25.7 −10.0 −9.5 −9.0 −9.2 −9.5 −7.0

Samples were first reported in ref 38. bBottlebrush samples labeled poly(aPP-NB)_DP. cFeed ratio. dDetermined by SEC-MALLS in tetrahydrofuran. eMn was determined by end-group analysis of 1H NMR spectrum. Mw determined as Mn × Đ. fWeight-average degree of polymerization of poly(norbornene) backbone using Mbranch = 2.05 kg/mol. gTg midpoint value measured by DSC. hLinear aPP sample provided by ExxonMobil Chemical Company. a

loading may be a result of catalyst deactivation, which becomes more consequential with longer reaction times. Thermal analysis of the polymers was conducted using differential scanning calorimetry, and thermograms of each polymer sample are presented in Figure S5. The Tg value of all poly(aPP-NB)s remains approximately constant, regardless of the backbone molar mass, and is within 3 °C of the Tg measured for aPP_Linear. This demonstrates that the Tg of bottlebrush molecules is dictated by the side chains and is independent of backbone chemistry and length.40,41 This is also consistent with the results of López-Barrón et al., which show that the Tg of aPP bottlebrushes trend toward that of linear aPP in the limit of high side chain length.37 Because of its low molar mass, the aPP-NB sample displayed a more depressed Tg value of −25.7 °C. This is in agreement with literature values of low molar mass linear aPP.42 Each of the samples listed in Table 1 were tested using smallamplitude oscillatory shear measurements at sufficiently low strain amplitudes to probe only the linear viscoelastic regime. The dynamic storage modulus (G′) and loss modulus (G″) were measured at various temperatures over a frequency range of 0.01−100 rad/s. In all cases data collected at different temperatures were superimposed by shifting G′(ω) and G″(ω) along the logarithmic frequency axis to an arbitrary reference temperature Tref = Tg + 34 °C. This procedure of time− temperature superposition (TTS) produced continuous dynamic master curves that encompassed the entire relaxation profile from glassy to terminal flow. The use of Tref = Tg + 34 °C accounts for any disparities in Tg among samples and represents room temperature dynamics of poly(aPP-NB)s (Tg ≈ 9 °C). Master curves of aPP-NB and all five poly(aPP-NB) samples are shown in Figure 2, and the applied TTS shift factors (aT) are plotted in Figure 3. The shift factors were fitted using the Williams−Landel−Ferry (WLF) relationship: log(aT) = −C1(T − Tref)/[C2 + (T − Tref)].43 Shift factors from all aPP samples (including the aPP_Linear control) were fit with a single set of WLF parameters: C1 = 7.6 and C2 = 85 °C. This suggests that the aPP materials exhibit dynamic responses with equivalent temperature dependence, irrespective of the branching structure. Each master curve shown in Figure 2 demonstrates a predominantly viscous response to the imposed deformation, as G″ remains greater than G′ at nearly all frequencies. The aPPNB macromonomer sample exhibits liquid-like behavior and shows a smooth transition from glassy to terminal relaxation. This is due to its low molar mass, which is below the entanglement threshold for aPP (Me = 3500−4500 g/

Figure 2. Dynamic master curves of G′ (closed symbols) and G″ (open symbols) for aPP-NB and poly(aPP-NB)s at a reference temperature of Tref = Tg + 34 °C. Curves vertically shifted using the indicated scale factors. The master curve for aPP_Linear is presented in Figure S6.

mol).44−46 The poly(aPP-NB) samples display a more pronounced Rouse-like relaxation at intermediate frequencies, where the breadth of this intermediate region widens as the backbone DP is increased. This expansion is consistent with the behavior of linear polymers in that increasing the polymer size causes an increase in the longest relaxation time and a delayed crossover to terminal behavior. However, unlike high molar mass linear polymers, no rubbery plateau is evident in any of the poly(aPP-NB) master curves, which suggests that the poly(aPP-NB)s remain unentangled even at molar masses greater than 106 g/mol. This is a consequence of the steric crowding among closely spaced side chains, which hinders the flexibility of the backbone chain and creates persistent brush C


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rad/s. The aPP_Linear displays a prominent rubbery plateau characteristic of a well-entangled polymer melt, which persists for several decades in reduced frequency before ultimately entering terminal flow. Moreover, note that the molar mass of aPP_Linear is nearest to poly(aPP-NB)_74 in the bottlebrush series and is an order of magnitude lower than poly(aPP-NB) _732. The fact that aPP_Linear displays the longest terminal relaxation time despite its moderate size illustrates a very weak dependence of terminal relaxation time on overall molar mass for the aPP bottlebrushes. This coincides with the relationship of zero-shear viscosity versus molecular weight (η0 ∼ Mwα) observed in these samples, in which the power law exponent remains low (α ≤ 1.2) at all molecular weights.38 Since neither the side chains nor the backbones of poly(aPP-NB)s form entanglement networks, the rheological dynamics of these molecules in the bulk state remain much faster than linear aPP analogues. Linear Rheology of PEP Bottlebrushes. To compare the linear viscoelastic behavior of systems with and without side chain entanglement, a second series of bottlebrush polymers were prepared from PEP-NB macromonomers (referred to as poly(PEP-NB)s). PEP was chosen because it is chemically similar to aPP but has a much lower entanglement molar mass (Me = 1930 g/mol).45 Thus, side chain entanglement could be promoted without requiring exceptionally long branches. Molecular characterization results of PEP-NB and the poly(PEP-NB) samples are given in Table 2.

Figure 3. Time−temperature superposition shift factors and WLF fit of the data (black line) at reference of Tref = Tg + 34 °C.

molecules with large cross-sectional areas. The backbone chain length required for entanglement in the bottlebrush melts is therefore much longer than the chain length of linear polymers, and the entanglement molar mass is increased by orders of magnitude. A very rough estimate of the expected value of Me for this series can be calculated according to the approach by Fetters et al. using the average molar mass per backbone bond.65 This calculation yields Me = 1.5 × 107 g/mol, which is an order of magnitude greater than the largest poly(aPP-NB) sample. A direct comparison between the bottlebrush polymers and aPP_Linear is more easily visualized with an overlay of the storage modulus master curves as presented in Figure 4. Each

Table 2. Molecular and Thermal Characterization of PEP Samples samplea PEP-NB poly(PEP-NB)_13 poly(PEP-NB)_125 poly(PEP-NB)_627

Mwb (kg/mol) 7.2 89 840 4200

c

Đb

DPd

Tge (°C)

1.08 1.06 1.23 1.57

13 125 627

−60 −59 −58 −58

a

Bottlebrush samples labeled poly(PEP-NB)_DP. bDetermined by SEC-MALLS in tetrahydrofuran. cMn was determined by end-group analysis of 1H NMR spectrum. Mw determined as Mn × Đ. dWeightaverage degree of polymerization of poly(norbornene) backbone using Mbranch = 6.7 kg/mol. eTg midpoint value measured by DSC.

The dynamic moduli of poly(PEP-NB) samples were measured, and master curves were constructed by TTS. Master curves for PEP-NB and each poly(PEP-NB) are plotted in Figure 5, and the shift factors are plotted in Figure 6. Once again the TTS shift factors converge onto a single WLF fit when plotted against T − Tg, yielding fit parameters of C1 = 8.4 and C2 = 110 °C. Since there are negligible differences in Tg values between the four samples, the single WLF fit indicates equivalent temperature dependences of the dynamic moduli for each of the PEP samples. The Tref for these samples was chosen to most closely match the Tref of the aPP series while still using an unshifted data set as the reference. In this case the frequency sweep data of poly(PEP-NB)_125 at −20 °C are used as the reference data set, giving a common reference temperature of Tref = Tg + 38 °C. The master curves in Figure 5 resemble those of poly(aPPNB)s in Figure 2 with the addition of rubbery plateau regions from 101 to 103 rad/s, which attest to the formation of entanglements among the PEP branches. This results in a resolved time-scale separation between the different relaxation modes, i.e., glassy, side chain, and terminal relaxation processes.

Figure 4. Storage modulus master curves of aPP-NB, poly(aPP-NB)s, and aPP_Linear at a reference temperature of Tref = Tg + 34 °C.

of the aPP samples exhibits indistinguishable behavior in the glassy-to-rubbery transition zone. This regime is associated with localized relaxations on the length scale of monomeric segments. Since aPP side chains constitute more than 95 wt % of poly(aPP-NB)s, it is reasonable that uniform segmental relaxation emerges. A clear deviation between aPP_Linear and poly(aPP-NB)s begins to develop at a reduced frequency of 104 D


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highlights differences in plateau regions and locations of terminal flow regimes.

Figure 7. Storage modulus master curves of PEP samples at a reference temperature of Tref = Tg + 38 °C. Figure 5. Dynamic master curves of G′ (closed symbols) and G″ (open symbols) for PEP samples at a reference temperature of Tref = Tg + 38 °C. Curves are vertically shifted using the indicated scale factors.

Master curves of the three poly(PEP-NB) samples show identical behavior throughout the plateau regions. This is because they are all entangled to the same degree due to the equivalent side chain lengths. However, the large disparity in backbone length leads to differences in the intermediate regimes of the master curves (i.e., between the plateau and terminal flow zones). Poly(PEP-NB)_13 displays practically no intermediate regime and transitions to terminal flow immediately following the plateau region. This molecule is approximately star-like in configuration and does not reveal any backbone relaxation effects. The poly(aPP-NB)_125 and poly(aPP-NB)_627 samples become progressively more representative of cylindrical bottlebrushes, leading to extended intermediate regions. The ultimate changeover to terminal flow is delayed to longer relaxation times and lower modulus values with increasing backbone length, and there is no evidence of a secondary plateau that would correspond to backbone entanglement. These characteristics are consistent with the behavior of the aPP bottlebrushes in that the relaxation profiles are qualitatively Rouse-like throughout the intermediate regime. The master curve for PEP-NB overlaps well with the poly(PEP-NB)s at high frequencies, signifying equivalent glassy relaxation dynamics, but the plateau region is truncated relative to the poly(PEP-NB)s, suggesting a lower degree of entanglement. This occurs because PEP-NB has only half the chain length as the diameter of the poly(PEP-NB) brushes. It may be more appropriate to compare the side chain relaxation dynamics (plateau region in this case) of the poly(PEP-NB)s with a linear PEP of twice the chain length as PEP-NB. This would represent the “dimer” or, equivalently, a poly(aPP-NB) with a backbone DP of 2. According to reptation scaling, a master curve of the dimer would simply display a plateau region that extends to a frequency about 23 = 8 times lower than that of PEP-NB. By inspection of Figure 7, we see that this dimer master curve would exhibit the same plateau width as the bottlebrush samples and overlay very closely with the poly(PEP-NB)_13. This is an interesting result because it

Figure 6. Time−temperature superposition shift factors for PEP samples (markers) and WLF fit of the data (line) at reference of Tref = Tg + 38 °C.

Previous studies on comb polymer melts with lower grafting densities also have revealed linear rheological spectra with complete separation of branch relaxation and backbone relaxation modes;19,21,47 however, these systems achieve significant branch and backbone entanglement due to the sparse branch spacing. Other groups have created bottlebrush polymers with greater side chain lengths; significantly, these systems did not produce branch entanglement due to the high Me of the branches in those systems.34,36,48−50 An overlay of storage modulus master curves is presented in Figure 7 and E


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Figure 8. (a) Reduced complex viscosity versus reduced frequency of aPP-NB (squares), poly(aPP-NB)_11 (right triangles), poly(aPP-NB)_26 (circles), poly(aPP-NB)_74 (diamonds), poly(aPP-NB)_215 (inverse triangles), and poly(aPP-NB)_732 (triangles) at a reference temperature of Tref = Tg + 34 °C. Reproduced with permission from ref 38. (b) Reduced complex viscosity versus reduced frequency of PEP-NB (circles), poly(PEP-NB)_13 (diamonds), poly(PEP-NB)_125 (inverse triangles), and poly(PEP-NB)_627 (triangles) at a reference temperature of Tref = Tg + 38 °C.

the backbone is bulk-like behavior retained? This system serves as a good test of the limits because it utilizes amorphous side chains with low inherent Me and promotes entanglement formation near to the backbone where branches are most crowded. The fact that the branches of poly(PEP-NB)s successfully form entanglements demonstrates that the packing constraints of this system are not sufficient to disrupt side chain overlap. To experimentally reach the limits in which entanglements would be completely inhibited by side chain crowding, bottlebrushes with lower branch Me and Mn or with greater branch density are required. Scaling Behavior of Bottlebrush Relaxation. Until this point we have described the relaxation of bottlebrush molecules in the intermediate scaling regime as qualitatively Rouse-like. We now focus more closely on this scaling behavior. Based on the classic theoretical Rouse and Zimm models,52,53 the scaling of dynamic moduli at intermediate frequencies follow the relationships

implies that poly(PEP-NB)s with backbone DP = 2 and DP =13 display the same linear viscoelastic profile at all relaxation times. There are two possibilities as to how this behavior might arise. One possibility is that every molecule in the series between DP = 2 and DP = 13 has nearly identical dynamics, and each master curve would overlay with poly(PEP-NB)_13 in Figure 7. Alternatively, it is possible that molecules successive to DP = 2 (e.g., DP = 3 or 4) would show even further extended plateau regions and longer terminal relaxation times than DP = 2 due to an increased reptation time of star polymers relative to linear polymers.6,51 In this case, however, the master curves of more successive polymers in the series (e.g., DP = 9 or 10) would necessarily revert back in order to retain the master curve of the DP = 13 sample. This effect could be rationalized as a result of the increased degree of side chain crowding with higher DP brushes. The increasingly compact molecular conformation could cause a slight reduction in the number of effective entanglements and reproduce the dynamics of DP = 2 at higher DP values. Experimental exploration of the molecules in this range, i.e. poly(macromonomer)s with DP = 3, 4, 5, etc., would help to clarify this issue but would likely require alternative synthetic strategies to ensure a precise number of branches per molecule. Although our goal was to create bottlebrushes with side chain entanglement, it was not obvious a priori that effective entanglements could develop in a system with such dense packing of side chains. For instance, a bottlebrush with an extreme graft density of one branch (or more) per backbone carbon would certainly preclude the ability of branches from neighboring brush molecules to interdigitate sufficiently for entanglement, particularly for branch segments near to the backbone. (Here we note that the mass density of the polymer melt, governed by the packing of segments at the subnanometer scale, is essentially unaffected by the molecular architecture.) Of course, packing constraints are relieved as side chains meander further out from the backbone since the available area per branch increases with the square of radial distance. Thus, side chains begin to exhibit increasingly bulk-like behavior further from the backbone. The question then becomes, how far from

Rouse:

G′(ω) ≅ G″(ω) ∼ ω1/2

(1)

Zimm:

G′(ω) ≅ G″(ω) ∼ ω 2/3

(2)

Equivalently, the scaling of the dynamic complex viscosity for these models is given as Rouse:

η*(ω) ∼ ω−1/2

(3)

Zimm:

η*(ω) ∼ ω−1/3

(4)

where complex viscosity is obtained from the dynamic frequency data as η*(ω) =

G*(ω) ω

(5)

Both of these models were initially developed to describe the dynamics of polymers in dilute solutions. The Zimm model predicts faster relaxation behavior than the Rouse model and provides a better description of real polymer solutions. This is because the Zimm model corrects the scaling law of the Rouse F


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Macromolecules model by incorporating effects of hydrodynamic interactions, i.e., the cooperative motion of segments within a polymer coil as mediated by disturbances of the surrounding flow field. By accounting for hydrodynamic interactions, the Zimm model depicts nondraining behavior in which internal polymer segments are shielded from the exterior of the coil and do not contribute viscous drag to the system. Alternatively, the Rouse model neglects these hydrodynamic interactions and predicts a free-draining system in which all polymer segments contribute equally to the overall viscosity. The Rouse model does, consequently, describe the behavior of unentangled polymer melts quite well since hydrodynamic interactions are screened by segments of overlapping polymer chains in the melt state. The physical pictures of the two models are reintroduced here in order to assess their validity in describing the behavior of bottlebrush systems. We chose to examine the complex viscosity master curves of the bottlebrush samples to evaluate their scaling behavior. These plots reflect equivalent data to the complex modulus (G*) master curves and can be compared with the Rouse and Zimm models using eqs 3 and 4, respectively. Figure 8 displays the complex viscosity master curves for each bottlebrush along with the macromonomer samples. The complex viscosity curves in Figure 8 overlap at high frequencies due to the equivalent segmental relaxation behavior. The low-frequency behavior is coincident with the transitions seen in the storage modulus overlays in Figures 4 and 7. The macromonomer samples achieve zero-shear viscosity at higher frequencies than the bottlebrushes, which display extended intermediate scaling regimes with increasing backbone DP. Given that each master curve displays uniform behavior at frequencies greater than the respective terminal flow regions, we can isolate the highest molar mass samples for both the PEP and aPP series to analyze the full relaxation spectrum and quantify the scaling behavior at different relaxation times. Figure 9a displays the complex viscosity master curve of poly(PEP-NB)_627. Between the glassy and terminal flow regions, this sample exhibits a steep scaling regime corresponding to the rubbery plateau as well as an intermediate scaling regime that spans about 3.5 decades in frequency. If we assume constant power law scaling (η* ∼ ωx), the intermediate regime is characterized by x = −0.33 as indicated on the plot as a slope of −1/3, which parallels the scaling predicted by the Zimm model. Additionally, we have calculated the instantaneous slope at each point along the master curve and plotted that data on a secondary y-axis. To reduce noise in the data due to random error at each data point, the instantaneous slopes were calculated by averaging the slope of the ten nearest data points surrounding the data point of interest (see Supporting Information for averaging method). Plotting the instantaneous slopes throughout the intermediate regime reveals that the slope of −1/3 arises as the average of a nonconstant scaling. The instantaneous slope actually falls monotonically to lower values (more negative) as the frequency is decreased. Figure 9b corresponds to poly(aPP-NB)_732, which has the widest intermediate scaling regime of any sample in this study (spanning more than 4 decades in frequency) due to its large ratio of backbone length to brush diameter. The instantaneous scaling of this sample also changes throughout the intermediate regime. The power law exponent continually becomes more negative with decreasing frequency and slowly approaches the Rouse model scaling prediction of x = −0.5. These results

Figure 9. Reduced complex viscosity versus reduced frequency of poly(PEP-NB)_627 (a) at a reference temperature of Tref = Tg + 38 °C and of poly(aPP-NB)_732 (b) at a reference temperature of Tref = Tg + 34 °C. The instantaneous slope of the complex viscosity data is included in both plots on a secondary vertical axis (circles).

demonstrate that the previous description of bottlebrush polymer relaxation as Rouse-like, both in this work and in previous reports, is not strictly representative of the entire relaxation process. Figure 9a shows that the poly(PEP-NB)_627 sample displays largely Zimm model scaling in the intermediate regime. By analogy with the Zimm model, this suggests the presence of shielded polymer segments that do not contribute to viscous drag. Unlike the Zimm model, however, the observed shielding effect does not arise due to hydrodynamic interactions. Instead, this results from the compact, space-filling conformation of the bottlebrush molecules at small length scales. The dense spacing of covalently bonded side chains along the backbone creates a high self-concentration and shields internal segments from contacting surrounding molecules, despite the close proximity of neighboring molecules in the undiluted state. It is not justifiable, though, to simply apply the specific scaling of the Zimm model to this system. The true dynamics of the system are dependent on the conformations of the individual bottlebrush molecules, which are conditional depending on the DP of the backbone. For instance, poly(macromonomer)s with short backbones are more starG


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Figure 10. Van Gurp−Palmen plots of (a) poly(aPP-NB)s and (b) poly(PEP-NB)s. Data for poly(aPP-NB)s are composite from all measurements taken at temperatures above 0 °C. Low-temperature data for poly(aPP-NB)s are given in Figure 12. Poly(PEP-NB)s include data at all temperatures measured.

Figure 10a shows the van Gurp−Palmen plots of poly(aPPNB)s. The minimum in phase angle near G* ∼ 106 Pa corresponds to the relaxation of aPP side chains. The location of this minimum is fixed since the side chain length is constant for all poly(aPP-NB)s. The second minimum at lower modulus pertains to the relaxation process of the entire bottlebrush molecule. This relaxation is distinct between the five poly(aPPNB)s and becomes more pronounced with increasing backbone length. In fact, the second minimum is not distinguishable for poly(aPP-NB)_11 and poly(aPP-NB)_26 due to the short backbones. The longest relaxation time of the side chains dominates the dynamics of these samples, and only one distinct minimum is observed. Poly(PEP-NB)s are represented in Figure 10b. The side chain relaxation process is very well-defined in these samples, marked with a sharp minimum at G* ∼ 106 Pa, indicative of a rubbery plateau region. Once again the side chain relaxation is uniform among the three samples due to the fixed side chain lengths. The low-modulus region shows the same trend as the poly(aPP-NB) samples; i.e., a second minimum in the phase angle steadily grows with increasing backbone DP, indicating a more pronounced relaxation of the entire bottlebrush. Comparing the plots in Figure 10, it appears that the prominence of the longest relaxation mode is dictated by the aspect ratio of the bottlebrush (i.e., the ratio of backbone length to side chain length). This can be quantified using the δ value of the second minimum. For example, poly(aPP-NB)_732 displays a more defined (lower δ value) longest relaxation mode than poly(PEP-NB)_627, despite the latter having higher overall molar mass. This is because poly(aPP-NB)_732 has the higher length-to-diameter aspect ratio. Additionally, poly(PEPNB)_627 exhibits a comparably defined longest relaxation mode to the much smaller poly(aPP-NB)_215. These two samples have similar aspect ratios and achieve minimum phase angle values of 59° and 58°, respectively. It is clear, however, that the separation between the two relaxation modes is greatest for poly(PEP-NB)_627 because the modulus of the slowest relaxation mode is regulated by total molar mass. Figure 11 explicitly shows this relationship with an overlay of the largest aPP and PEP bottlebrush samples.

like and should display different dynamics than more cylindrical molecules with longer backbones. Thus, the dynamics of bottlebrush polymers should exhibit transient scaling at different relaxation times. Shorter times correspond to more compacted star-like sections, and longer times correspond to the relaxation of elongated (conformationally cylindrical) brush sections. Such transient scaling behavior is best demonstrated in Figure 9b. At the highest frequency associated with the intermediate regime (early relaxation times), the instantaneous scaling is actually faster than the Zimm model prediction (note: the limit of fast dynamics would yield a slope of 0, indicating a fixed viscosity value). The magnitude of the instantaneous slope continually becomes more negative at lower frequencies, passing through the Zimm model scaling value and reflecting the continually changing conformational state of bottlebrushes at longer length scales. Any relaxation time in which exact Zimm scaling is recovered is coincidental and does not imply that the Zimm model portrays the same physical situation. Ultimately, Rouse dynamics are expected to be retained in the limit of backbone lengths much greater than the bottlebrush diameter. In this limit, the bottlebrush can be viewed as very thick Gaussian chain that is long enough to retain random-walk conformations. Van Gurp−Palmen Analysis: Sequential Relaxation. Figure 10 presents the dynamic response data for the poly(aPPNB) and poly(PEP-NB) samples plotted as the phase angle (δ) versus the complex modulus (G*). Van Gurp and Palmen initially proposed this type of representation as a tool to verify the applicability of TTS for specific polymer materials.54 More recent studies have demonstrated the utility of the “van Gurp− Palmen” plot in elucidating structural information such as molar mass, dispersity, and branching content as well as detecting the presence of multiple relaxation processes.55,56 Specifically, a polymer melt with two distinct relaxation modes will generate a bimodal curve with two separate minima as occurs in many branched polymer systems, leading to a sequential relaxation mechanism.14,20,23,34−36,57,58 Since the individual relaxations of the side chains and of the backbones both contribute to the dynamic response profiles of bottlebrush polymers, the van Gurp−Palmen plot serves as a useful tool for analyzing the bulk rheology. H


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bottlebrush aspect ratio, while the modulus of this mode is dictated by the total molar mass. As a result, the slowest relaxation mode of poly(aPP-NB)_732 emerges at a lower minimum phase angle but a greater modulus than that of poly(PEP-NB)_627. The dashed vertical lines in Figure 11 mark the modulus values of the local minima. Comparing these two values gives a good estimate of the difference between longest relaxation moduli of the two samples but does not indicate the absolute modulus values for the slow relaxation process. A more accurate determination of the slowest relaxation modulus is achieved by locating the G* value at the inflection point of the curves, which indicates the start of the terminal flow region.55 The slowest relaxation modulus can be estimated by

G=

ρRT M total

(6)

where ρ, R, T, and Mtotal are the density, gas constant, temperature, and total bottlebrush molar mass, respectively. The solid lines in Figure 11 identify the anticipated modulus value of the slowest mode calculated using eq 6 and assuming literature values for the bulk density of aPP and PEP at T = 298 K.45 The predicted modulus for both samples is in good agreement with the data, as both solid lines are in close proximity to the inflection points of the curves. This supports the applicability of eq 6 and confirms that the entire bottlebrush molecule controls the slowest relaxation mode.

Figure 11. Van Gurp−Palmen plot of poly(PEP-NB)_627 (triangles) and poly(aPP-NB)_732 (diamonds). Solid lines mark the modulus estimated using eq 6. Dashed lines denote the modulus of the local minimum.

Figure 11 provides a direct comparison between poly(PEPNB)_627 and poly(aPP-NB)_732 and highlights features of the van Gurp−Palmen plot that help to elucidate details of different relaxation processes. Specifically, the minimum phase angle of the slowest relaxation mode is dependent on

Figure 12. Van Gurp−Palmen plots of the dynamic response measurements for poly(aPP-NB)_732 (a), poly(aPP-NB)_215 (b), poly(aPP-NB)_74 (c), and poly(aPP-NB)_26 (d) at indicated temperatures. I


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for entanglement of bulk PEP (M n /M e ≈ 3.5). We hypothesized, despite the sufficient length of PEP chains, that intermolecular entanglements might be inhibited in these materials due to the close spacing of branches and the relatively low Me of PEP chains that favors entanglement formation near the crowded backbone. However, side chain entanglement was realized in each of the polymers in this series. Detailed analysis of the dynamic modulus and viscosity data revealed a transient scaling behavior throughout the relaxation spectra of the largest bottlebrush polymer in each series. This behavior is a result of the conformational states of bottlebrushes at different length scales. At early relaxation times the dynamics are more Zimm-like due to the compact arrangement of polymer segments at small length scales. In this regime, many of the internal segments near the backbone are shielded from neighboring molecules. This is fundamentally different but effectively similar to the shielding of internal segments due to hydrodynamic interactions described by the Zimm model. The relaxation scaling becomes more Rouse-like at longer times, as the molecules more closely resemble elongated cylinders. Bottlebrushes at larger length scales can be described as dynamically analogous to unentangled Gaussian chains. Van Gurp−Palmen plots of the rheological data were used to further resolve details of the two relaxation processes, i.e., distinct side chain and backbone relaxations. The relative influence of each relaxation mode on the system dynamics can be visualized as minima in the van Gurp−Palmen plot. Each of the poly(PEP-NB)s displayed a much more elastic (indicated by lower minimum phase angle value) side chain relaxation mode than poly(aPP-NB)s due to the presence of entanglements. The longest relaxation mode within each series became more prominent as the backbone DP was increased. The modulus value corresponding to the longest relaxation mode is dictated by the overall bottlebrush molar mass and can be estimated by identifying the inflection point of the van Gurp− Palmen plot. Alternatively, the phase angle value of the slowest mode depends on the length-to-diameter aspect ratio of the bottlebrush molecules. Van Gurp−Palmen analysis also highlights the onset of thermorheological complexity in the aPP samples. This behavior is consistent with the behavior of linear aPP and suggests that the highly branched architecture of bottlebrushes does not significantly affect the thermal transitions of the materials in the bulk state.

Van Gurp−Palmen Analysis: Thermorheological Complexity. As mentioned previously, the van Gurp−Palmen plot was originally recommended to validate the application of TTS. Since the frequency axis is eliminated in this type of plot, the effect of shifted relaxation times at different temperatures is removed. Therefore, if the material is thermorheologically simple (i.e., relaxation modes have equivalent temperature dependences), then data taken at all temperatures will converge onto a continuous curve without application of arbitrary shift factors. For clarity in demonstrating the double relaxation phenomenon, the data plotted in Figure 10a excluded any measurements taken at or below 0 °C. Figure 12 displays the complete van Gurp−Palmen plots for several of the poly(aPPNB) samples. Clearly the inclusion of low-temperature data reveals discontinuities between measurements taken at different temperatures, indicating thermorheologically complex behavior as the Tg is approached. Thus, TTS is not strictly applicable to the low temperature data despite the ostensibly seamless master curves in Figure 2. These complexities were not as significant for the poly(PEP-NB) series; thus, data from all temperatures measured are included in Figure 10b. Thermorheological complexity near the glass transition has been reported in many linear polymer materials, including poly(styrene),59 poly(isobutylene),60 and aPP.46 Plazek first investigated the linear viscoelasticity of aPP using creep deformation experiments. This material appeared to be thermorheologically simple based on the ability to construct a continuous master curve spanning 13 decades of reduced time. However, the authors described the initial apparent thermorheological simplicity as fallacious. It was hypothesized that drawn-out creep measurements at temperatures “in the neighborhood of 0 °C” would display poor reducibility when applying TTS.46 This conclusion is consistent with the data shown in Figure 12 for poly(aPP-NB)s. Near 0 °C the value of δ begins to increase at fixed G* as the temperature is decreased closer to Tg. These low-temperature measurements were repeated for two of the poly(aPP-NB)s using much smaller (3 mm diameter) rheometer plates to reduce any effects of instrument compliance.61 The data displayed the same discontinuities in van Gurp−Palmen plots as those in Figure 12, confirming the apparent thermorheological complexity as an inherent property of the materials (Figures S13 and S14). Though a concrete theoretical explanation of this complex behavior remains elusive (and an ongoing topic of debate),62 it is remarkable that the same observations are found in linear and bottlebrush aPP materials. Along with the value of Tg and the high-frequency dynamic behavior, the thermorheological nature of bottlebrush polymers appears to be governed by the chemistry of monomeric repeat units and independent of the macromolecular architecture.

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EXPERIMENTAL SECTION

Materials. Chemicals that were purchased from Sigma-Aldrich and used as received include 9-borabicyclo[3.3.1]nonane (9-BBN; 0.5 M in THF), triethylamine, oxalyl chloride, exo-5-norbornenecarboxylic acid ((1R,2S,4R)-bicyclo[2.2.1]hept-5-ene-2-carboxylic acid), Cl 2 (3BrPy)2(H2IMes)RuCHPh (G3), dibutylmagnesium, n-butyllithium, sec-butyllithium, tetrahydrofuran (THF), toluene, and methanol. Chemicals used in anionic polymerization including isoprene and ethylene oxide were purchased from Sigma-Aldrich and purified according to literature procedures.63 Vinyl-terminated atactic polypropylene (aPP) was obtained from ExxonMobil Chemical Company. The received aPP sample (Mn = 859 g/mol; Đ = 1.88) was precipitated into a large volume of methanol for purification. Precipitation resulted in the removal of the low molar mass aPP fractions, yielding a sample with Mn = 1750 g/mol and Đ = 1.65 after precipitation. 1H NMR spectroscopy after precipitation (500 MHz, CDCl3, 25 °C): δ = 5.81 ppm (dq, 1H), 5.01 ppm (m, 2H), 2.07 ppm (m, 1H), 1.89 ppm (m, 1H), 0.60−1.80 ppm (m, 245H). The 1H NMR spectrum is given in Figure S1. Synthesis. Hydroxyl-Terminated Atactic Polypropylene (APPOH). Vinyl-terminated aPP was converted to aPP-OH via consecutive

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CONCLUSION Two series of polyolefin-based bottlebrush polymers were prepared by ROMP of norbornene-terminated macromonomers in order to investigate the effects of side chain length and backbone length on the linear rheological behavior. The first series included bottlebrushes with aPP side chains of Mn = 2.05 kDa, which is below the entanglement spacing of linear aPP in the melt state (Mn/Me ≈ 0.5). Dynamic master curves of these samples do not exhibit plateau regions at any point between glassy relaxation and terminal flow, indicating no side chain or backbone entanglement. The second series utilized PEP side chains of Mn = 6.7 kDa, which exceeds the critical molar mass J


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procedure was iterated several times until the solution was at 35 °C. After the final heat, stirring was stopped and the solution was allowed to cool slowly back to room temperature. High molar mass bottlebrush polymers precipitated easily out of solution. Molecular Characterization. 1H NMR spectra were acquired on a Bruker Avance III 500 MHz spectrometer in a CDCl3 solvent. Size exclusion chromatography (SEC) analysis was performed using an Agilent 1260 Infinity LC system equipped with three Waters Styragel columns in series, a Wyatt DAWN Heleos II 18-angle laser light scattering detector, and a Wyatt OPTILAB T-rEX refractive index (RI) detector. SEC samples were analyzed at 25 °C in a THF mobile phase at a flow rate of 1.0 mL min−1. Absolute molar masses of the aPP-NB macromonomer and poly(aPP-NB) samples were determined using the in-line light scattering detector with a dn/dc = 0.079 mL/g.64 Absolute molar mass determination of PEP-NB and poly(PEP-NB)s utilized a dn/dc value of 0.070 mL/g, as measured by the SEC instrument assuming 100% mass elution. Differential Scanning Calorimetry. Thermal analysis was performed using a TA Instruments Discovery DSC apparatus. Samples were first heated to 50 °C (10 °C/min), then slowly cooled below the glass transition temperature (to −50 °C for aPP samples; to −75 °C for PEP samples) at 5 °C/min, and finally heated a second time for analysis. Rheological Characterization. All samples were examined using a TA Instruments ARES rheometer. Samples were analyzed under nitrogen flow on either 8 or 3 mm diameter parallel plates. All samples were first submitted to dynamic strain sweep analysis to determine the linear viscoelastic regime of the materials. Small-amplitude oscillatory shear (SAOS) measurements were then carried out at strains low enough to remain within the linear viscoelastic region and a frequency range of 100−0.01 rad/s. Master curves were constructed by shifting data along the frequency axis at a reference temperature of Tref = Tg + 34 °C for aPP samples and Tref = Tg + 38 °C for PEP samples. The reference temperature for aPP samples was chosen to reflect room temperature data of poly(aPP-NB)s. Specifically, frequency sweep measurements taken at 25 °C for poly(aPP-NB)_74 (Tg = −9 °C) were used as the reference data. For the PEP samples, measurements taken at −20 °C of the poly(PEP-NB)_125 sample (Tg = −58 °C) were chosen as the reference data.

hydroboration/oxidation of the terminal olefin as previously reported.30,38 Vinyl-terminated aPP (10 g, 5.7 mmol) was first dissolved in THF (50 mL) under an argon atmosphere. The solution was cooled to −20 °C before slowly adding a solution of 9-BBN in THF (25 mL, 12.5 mmol). After stirring for 18 h at room temperature, the solution was again cooled to −20 °C and methanol (5 mL) was added slowly. Aqueous sodium hydroxide (10 mL, 6 N) and hydrogen peroxide (14.2 mL, 125 mmol) were then added, and the solution was gradually heated to 40 °C and stirred for 4 h. The resulting solution was cooled to room temperature, and the solvent was removed by rotary evaporation. The residual polymer was dissolved in chloroform (50 mL), and the solution was washed once with dilute HCl (pH of 5) and three times with deionized water. The chloroform solution was then dried over magnesium sulfate. The product was precipitated into methanol (500 mL) at 0 °C and dried in vacuo. Yield: 8.71 g (87.1%). 1 H NMR (500 MHz, CDCl3, 25 °C): δ = 3.66 ppm (t, 2H), 0.60−1.80 ppm (m, 260H). The 1H NMR spectrum is presented in Figure S2. Norbornenyl-Functionalized Atactic Polypropylene (APP-NB). exo-5-Norbornenecarboxylic acid (10 g, 72 mmol) was dissolved in deoxygenated toluene (50 mL) in a 250 mL round-bottom flask under an argon atmosphere. Oxalyl chloride (6.2 mL, 72 mmol) was slowly added to the solution with constant stirring. Excess pressure in the reaction flask was relieved from the headspace using a bubbler. The reaction mixture was first stirred at room temperature for 30 min and then at 60 °C for 1 h and 70 °C for an additional 1 h before cooling back down to room temperature. Any remaining oxalyl chloride was removed under gentle vacuum along with ∼10% of the toluene solvent. In a separate flask triethylamine (10.3 mL, 73.8 mmol), aPPOH (25.5 g, 13.8 mmol), and toluene (125 mL) were mixed and degassed by consecutive freeze−pump−thaw cycles. This mixture was added to the reaction flask via cannulation. The resulting solution was heated to 100 °C and stirred for 12 h. The solution was then cooled down to room temperature, and the product was isolated by twice precipitating in copious amounts of methanol. 1H NMR (500 MHz, CDCl3, 25 °C): δ = 6.15 ppm (m, 2H), 4.09 ppm (m, 2H), 3.07 ppm (s, 1H), 2.95 ppm (s, 1H), 2.25 ppm (dd, 1H), 1.95 ppm (dt, 1H), 0.60−1.80 ppm (m, 276H). The 1H NMR spectrum is presented in Figure S3. Norbornenyl-Functionalized Poly(ethylene-alt-propylene) (PEPNB). Initially, ω-hydroxylpolyisoprene (PI-OH) was synthesized by anionic polymerization according to procedures detailed elsewhere.39,62 Hydrogenation of PI-OH (17 g) was then carried out in cyclohexane (500 mL) using a heterogeneous Pt−Re/SiO2 catalyst (3.2 g) under 500 psi of H2 at 100 °C and stirred for 12 h. The resulting ω-hydroxyl-PEP (PEP-OH) was further functionalized with exo-5-norbornenecarboxylic acid following the same protocol as the aPP-NB synthesis, detailed above. 1H NMR spectra (500 MHz, CDCl3, 25 °C) of PI-OH, PEP-OH, and PEP-NB are presented in Figures S7, S8, and S9, respectively. Bottlebrush Polymers via ROMP of Macromonomers. In a typical reaction, aPP-NB (1 g, 0.5 mmol) was added to a 20 mL scintillation vial and dissolved in degassed THF (15 mL). The vial was sealed with a rubber septum and purged with argon gas. In a separate scintillation vial, a stock solution of G3 in THF was prepared, and a desired amount was added quickly to the aPP-NB solution. The stock solution was used quickly after preparation to minimize the amount of catalyst deactivation upon dissolution in solvent. The reaction mixture was stirred for at least 10 min (longer times were required when targeting high molar mass) and quenched with excess ethyl vinyl ether. The product was purified by precipitation in methanol and dried under vacuum. All steps were carried out at room temperature. Poly(aPP-NB)s required no additional purification since quantitative conversion was achieved in most samples. Poly(PEP-NB) samples did not achieve complete conversion, presumably due to the higher molar mass of PEP-NB compared to aPP-NB, and the majority of the unreacted macromonomers were removed by fractionation procedures. Briefly, methanol was used as a nonsolvent and was added dropwise to a stirring solution of polymer in THF at room temperature until the solution became clouded. The temperature was then increased 2 °C and the solution clarified. The same

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ASSOCIATED CONTENT

S Supporting Information *

1

H NMR spectra, SEC traces, DSC thermograms, supplementary dynamic moduli data, and additional calculations. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01153.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (F.S.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS ExxonMobil Chemical Company provided the vinyl-terminated aPP precursors and the financial support for this work. We thank Carlos López-Barrón and Pat Brant for helpful discussions. We also thank Tim Gillard for providing the hydroxyl-terminated polyisoprene starting material. Parts of this work were facilitated by the Characterization Facility, University of Minnesota, which receives partial support from the NSF through the MRSEC program.

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Linear Rheology of Polyolefin-Based Bottlebrush Polymers

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