Consequences of Grafting Density on the Linear Viscoelastic Behavior

Letter Cite This: ACS Macro Lett. 2018, 7, 525−530

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Consequences of Grafting Density on the Linear Viscoelastic Behavior of Graft Polymers Ingrid N. Haugan,† Michael J. Maher,† Alice B. Chang,‡ Tzu-Pin Lin,‡ Robert H. Grubbs,‡ Marc A. Hillmyer,§ and Frank S. Bates*,† †

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States § Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States ‡

S Supporting Information *

ABSTRACT: The linear viscoelastic behavior of poly(norbornene)-graf t-poly(±-lactide) was investigated as a function of grafting density and overall molar mass. Eight sets of polymers with grafting densities ranging from 0 to 100% were synthesized by living ring-opening metathesis copolymerization. Within each set, the graft chain molar mass and spacing between grafts were fixed, while the total backbone length was varied. Dynamic master curves reveal that these polymers display Rouse and reptation dynamics with a sharp transition in the zero-shear viscosity data, demonstrating that grafting density strongly impacts the entanglement molar mass. The entanglement modulus (Ge) scales with inverse grafting density (ng) as Ge ∼ ng1.2 and Ge ∼ ng0 in accordance with scaling theory in the high and low grafting density limits, respectively. However, a sharp transition between these limiting behaviors occurs, which does not conform to existing theoretical models for graft polymers. A molecular interpretation based on thin flexible chains at low grafting density and thick semiflexible chains at high grafting density anticipates the sharp transition between the limiting dynamical regimes.

T

has been shown to afford precise control over grafting density (z), backbone degree of polymerization (nbb), and side chain degree of polymerization (nsc).36 Here we describe the copolymerization of ω-norbornenyl polylactide macromonomers (Mn = 3.5 kg/mol) with a norbornene dimethyl ester monomer leading to polymers with specified z and nbb at constant nsc and low dispersity (Đ < 1.2). Materials ranging from linear (z = 0) to fully grafted bottlebrushes (z = 1) were characterized rheologically, revealing how grafting density controls the melt state linear viscoelastic properties. The effect of grafting density was systematically studied in eight sets of graft polymers, prepared using methods described in the Supporting Information. Within each set, z was held constant, and nbb was varied. The viscoelastic behavior was measured using linear dynamic mechanical analysis. Dynamic master curves were created by time−temperature superposition (TTS) of the data relative to the reference temperature Tref = Tg + 34 °C. TTS assumes that the samples are thermorheologically simple, which was validated in four ways, as discussed further in the Supporting Information: (1) appearance of only one glass transition temperature (Tg) as determined by

he complex interplay between polymer architecture and macromolecular dynamics has profound consequences on material properties. Polymers with graft architectures have garnered significant interest due to their unique properties (e.g., low entanglement plateau1−5 and low viscosity6−8) and have found use in a variety of applications, including photonic crystals,9 battery membranes,10 lithography,11 and drug delivery.12 At high grafting density, crowding of the side chains13,14 (Figure 1) causes the polymer backbone to adopt an extended, wormlike conformation,15−22 resulting in drastically different physical properties than the linear counterparts. Extensive theoretical and experimental efforts have focused on translating the dynamics of linear polymers into models to describe and predict the associated physical properties.23−30 However, the underlying dynamics of graft architecturesin particular the transition from linear to combs to bottlebrush polymersis not well established. Ongoing theoretical efforts to develop a universal model of graft polymer dynamics1,31−35 have outpaced experimental studies due in part to the synthetic challenges associated with exercising control over grafting density. As a consequence, one key unresolved issue is how grafting densitydefined as the average number of graft chains per monomeric unit of backboneimpacts polymer conformation and physical properties. Recently, a grafting-through ring-opening metathesis copolymerization of macromonomers and small-molecule monomers © XXXX American Chemical Society

Received: February 9, 2018 Accepted: March 26, 2018

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DOI: 10.1021/acsmacrolett.8b00116 ACS Macro Lett. 2018, 7, 525−530

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ACS Macro Letters

Figure 1. Comparison of comb and bottlebrush molecular architectures and chain conformations. Scaling of backbone length between grafts, Lg, and side chain diameter, dsc, are shown for each case. (A) At low grafting densities the graft polymer has a comb conformation where the backbone and side chain are both unperturbed Gaussian coils; comb parameters are defined as Lg,0 and dsc,0. (B) At high grafting densities, the grafts and backbone are extended. In the bottlebrush limit the parameters are defined as Lg,s and dsc,s.

(nbb < 640) display two distinct relaxation regimes at low and high reduced frequency. At low reduced frequencies, all of the polymers exhibit terminal flow evidenced by G′ ∼ ω2, G″ ∼ ω, and G′ < G″. At high reduced frequencies, Rouse scaling of G′ ∼ G″ ∼ ω1/2 is observed,23 which is characteristic of unentangled polymer melts and has been previously reported for bottlebrush polymers.7,39−46 For the higher Mw samples in Figure 2 (nbb ≥ 640), a third regime is apparent at intermediate reduced frequencies, characterized by a plateau in G′ associated with molecular entanglements as predicted by the reptation model.26,27,47 Note that the side chains do not entangle because the graft chain molar mass is lower than the entanglement molar mass (Me) for polylactide.48 These observations are in good agreement with previous reports on sparsely grafted polymers.49,50 Zero-shear viscosities were obtained from the terminal portions of the dynamic master curves (η0 = G″/ω) and are plotted as a function of weight-average molar mass in Figure 3, where the data associated with the unentangled and entangled samples are shown with open and closed symbols, respectively. Nearly all of the data in Figure 3 can be fit using η0 ∼ Mwα with α of either 1 or 3, consistent with Rouse and reptation scaling, respectively. For the z = 0.25 series, an abrupt transition from Rouse to reptation scaling is clearly evident, demonstrating that graft polymers follow the same fundamental relaxation processes as linear polymers, where the crossover occurs at Mc ≅ 2−3 Me in which Me is the entanglement molar mass. The increased viscosities of the highest molar mass samples in the z = 0.50 and z = 1.0 series also are consistent with a transition to reptation scaling as shown in Figure 3. These results demonstrate that at a fixed overall Mw of the graft polymer η0 can be tuned over several orders of magnitude by adjusting the grafting density. Hu et al. observed a similar high viscosity sample that departed from Rouse scaling at high nbb and attributed this increase in viscosity of the high z bottlebrush to steady state compliance rather than backbone entanglements.40 However, the data in Figure 3 show a clear transition from Rouse to reptation scaling over a range of z, including the linear

differential scanning calorimetry; (2) no microphase separation between the grafts and backbone based on small-angle X-ray scattering; (3) fitting of all the data with the Williams−Landel− Ferry (WLF) model based on a single set of WLF parameters;37 and (4) continuity in van Gurp−Palmen plots of the data.38 Figure 2 shows the master curves of the storage (G′) and loss (G″) moduli for a representative set of graft polymers with z = 0.25 and varying nbb (other grafting density samples can be found in the Supporting Information). The low Mw samples

Figure 2. Dynamic master curves for z = 0.25 series. The backbone degree of polymerization (nbb) is labeled on the graph. Master curves have been shifted vertically by the factors on the right for clarity. 526

DOI: 10.1021/acsmacrolett.8b00116 ACS Macro Lett. 2018, 7, 525−530

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ACS Macro Letters Me =

ρRT Ge

(1)

Me increases monotonically from 11 kg/mol for z = 0 to 1600 kg/mol for z = 1 (Figure S10) and is the molar mass of the entire graft polymer between entanglements. Figure 4 shows the normalized entanglement modulus (Ge/Ge,lin) as a function of ng, where Ge,lin is the entanglement modulus of the z = 0 series. At low grafting densities (i.e., large values of ng), the graft polymers resemble a comb with unperturbed backbone and side chain conformations (Figure 1A). For both LC and DC regimes Ge is predicted to decrease with decreasing ng (increasing graft density) due to backbone dilution1 −3 ⎛ nsc ⎞ ⎟ Ge = Ge,lin⎜⎜1 + ng ⎟⎠ ⎝

(2)

⎛ n ⎞ where ⎜1 + nsc ⎟ is the inverse backbone volume fraction; eq 2 ⎝ g ⎠ is plotted in red in Figure 4. Daniel et al. distinguished LC and DC by their scaling, where LC scales as Ge/Ge,lin ∼ ng0 in the limit of nsc ≪ ng and DC scales as Ge/Ge,lin ∼ ng3 in the limit of nsc ≫ ng. Our data at low grafting density are more similar to the LC model because the scaling is much closer to ng0 than ng3. In the opposite limit, the DB (high grafting density, low ng) regime, the backbone and side chains are highly extended (Figure 1B), and Ge is predicted to scale as

Figure 3. Reduced zero-shear viscosity versus Mw with power law fits for six series of constant grafting density. Mw refers to the weightaverage molecular weight of the entire polymer chain. Unentangled and entangled polymers are shown with open and filled symbols, respectively.

series where z = 0. With the addition of zero-shear viscosity data for many z series, we conclude that the departure from Rouse scaling at high z indicates backbone entanglement. Daniel et al. developed scaling laws that predict how the entanglement modulus (Ge) varies as a function of volumenormalized inverse grafting density (ng) and nsc for four distinct conformational regimes (see inset of Figure 4): loose comb (LC), dense comb (DC), loose brush (LB), and dense brush (DB).1 For the series of graft polymers discussed in this letter, Ge was estimated from van Gurp−Palmen plots (Figure S9), where

⎛ ng ⎞3/2 Ge ∼ Ge,lin⎜ ⎟ ⎝ nsc ⎠

(3)

In this limit we find experimentally that Ge/Ge,lin ∼ ng , which is within experimental uncertainty of the theory. Based on these results, we classify the graft polymers in this study as DB and LC in the high and low grafting density regimes, respectively. One of the most striking features of the data in Figure 4 is the absence of the LB regime (Ge/Ge,lin ∼ ng0) and asymptotic scaling in the DC regime (Ge/Ge,lin ∼ ng3) predicted by the theory. In the LB regime the theory predicts that the backbone extends as grafting density increases to prevent the side chains from overlapping, but the conformation of the overall graft polymer does not change because the distribution of side chains remains constant. Due to the constant overall molecular conformation, Ge/Ge,lin is theorized to be invariant with respect to ng, which is not apparent in the experimental data. There is a sharp transition between the LC and DB regimes, but the magnitude of Ge/Ge,lin falls well below the values predicted by eq 2, indicating that the experimental results do not fit the model for DC. In fact, eq 2 predicts that the scaling limit of Ge/ Ge,lin ∼ ng3 is not reached until much lower values of ng, beyond even the DB regime. Therefore, the properties of the graft polymers with intermediate grafting density are not captured by either the theoretical DC or LB regimes. We propose that changes in the backbone conformation may explain the dramatic decrease in Ge/Ge,lin in the intermediate regime. In the melt state, the volume pervaded by a macromolecule depends on the flexibility of the chain. Stiffer polymers occupy a greater configurational volume than more flexible ones at constant backbone Mw. This volume-filling capacity influences the density of entanglements, hence Ge, which can be related to the statistical segment length, b. The packing length concept51 leads to the scaling relationship Ge ∼ b6. Thus, the sharp decrease in plateau modulus would 1.2

Figure 4. Normalized plateau modulus Ge/Ge,lin plotted versus inverse grafting density ng. The inset shows the scaling predicted by Daniel et al. for four regimes: dense brush (DB), loose brush (LB), dense comb (DC), and loose comb (LC), where the numbers identify the scaling exponents. This inset emphasizes the scaling of Ge/Ge,lin and does not predict the range of the regimes. The red curve shows the predictions of eq 2, which applies to the LC and DC regimes. These results indicate that the graft polymers transition abruptly from LC to DB and that the LB and low ng limit of the DC regimes are absent for the presented data. 527

DOI: 10.1021/acsmacrolett.8b00116 ACS Macro Lett. 2018, 7, 525−530

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ACS Macro Letters represent a decrease in b or an apparent increase in chain flexibility with increasing grafting density (Figure S12). The apparent decrease in b as grafting density increases can be explained by the conflation of the regime transition with other important physical parameters not considered in the original theory. The LC to DB transition regime occurs over a narrow window of ng (between 4 and 6 norbornene units between grafts on average), which is close to the Kuhn length (lK) for these polymers (calculated in eq S8). Instead, we suggest that the backbone kinks (i.e., folds back on itself) in order to space out the densely grafted side chains as illustrated schematically in Figure S13. This reduces b, consistent with a more “flexible” conformation, which would explain the observed decrease in Ge in this regime. Visualization of this kinking phenomenon could be accomplished via scattering or simulations and will be pursued in future experiments. Comparison of the experimental data and the theory exposes differences between real polymers and the ideal model polymers employed in developing the scaling models. For example, the Daniel et al. theory assumes that lK ≫ ng in all four scaling regimes. In practice, ng approaches lK prior to reaching the dense brush limit. Another idealization is that the graft chains are large enough to pervade a configurational volume significantly larger than the space occupied by the graft chain. However, the real side chains in our case are relatively short, with a coordination number (chains per coil volume) of just 5 (eq S13). As a consequence, the transition from barely overlapping to overly crowded side chains occurs across a rather narrow range of ng, essentially squeezing out the LB regime. In principle, increasing the length of the side chains would help reconcile this practical inconsistency between experiment and theory. However, increasing the length of the side chains can lead to graft chain entanglement, which complicates backbone relaxation.40,41,50,52−55 Moreover, side chain entanglement also negates the benefit of a reduced modulus associated with the dense brush limit, forfeiting any supersoft quality imparted on the material by the architecture. The practical reality of these physical phenomena obscures the predictions of the theory in the ideal limit. We propose a different method to predict the entanglement of graft polymers that relies on calculating two ratios: (1) the diameter of the side chains (dsc) to the average backbone length between grafts (Lg) and (2) the backbone degree of polymerization between entanglements (ne,bb) in the graft polymer normalized by degree of polymerization between entanglements of the linear polymer (ne,lin). Figure 1 shows how dsc and Lg scale in the LC and DB regimes. To account for the polymer conformation at the transition between these regimes, we assume that the backbone is extended, but the side chains remain unperturbed. Therefore ⎛ n ⎞1/2 dsc = 2R g,sc = 2b⎜ sc ⎟ ⎝ 6 ⎠

Figure 5. Entanglement data plotted as ne,bb/ne,lin vs dsc/Lg, where ne,bb/ne,lin is the ratio of the backbone units between entanglements normalized to the backbone units between entanglements for z = 0, and dsc/Lg is the ratio of the diameter of the side chain to the average distance between grafts. The black and blue lines identify the limits of low and high grafting densities, respectively, as illustrated schematically in Figure 1. When dsc/Lg > 1 steric interference between side chains leads to a reduction in the density of entanglements.

that occurs when dsc/Lg ≈ 1 or when the side chains begin to overlap. The two regimes in Figure 5 can be associated with a thin, flexible chain and a thick, semiflexible cylinder, as portrayed in Figure 1. In the comb regime, the flexible backbone resembles a linear polymer chain, and the conformation is largely dictated by the chemistry of the backbone. However, in the high grafting density bottlebrush limit, the backbone is shielded by the side chains, and the overall conformation resembles a thick cylinder. Here the conformation of the backbone is dictated by steric repulsion of the side chains and is driven by the molecular architecture rather than the chemistry. The transition between these regimes occurs when the side chains start to overlap, as estimated using an unperturbed Gaussian coil side chain and extended backbone. For graft polymers with physically relevant (i.e., relatively short) side chain lengths, this model appears general. The consequences of side chain overlap with increasing grafting density have also recently been demonstrated in the context of block polymer self-assembly.56 In conclusion, the linear viscoelastic response of eight sets of polymers with variable grafting density was studied, demonstrating that at high grafting density the polymers behave as dense bottlebrushes (DB), where Ge ∼ ng1.2, in reasonable agreement with theory. Reducing the grafting density results in a sharp transition to a loose comb (LC) regime. We propose a simple criterion for anticipating the onset of entanglement dynamics in graft polymers based on dsc/Lg, the ratio of the diameter of gyration of the side chains to the average backbone contour length between grafts. When dsc/Lg < 1 the polymers behave as thin flexible chains with conformations dictated by the backbone chemistry, while dsc/Lg > 1 leads to thick semiflexible cylinders and a chain configuration governed by the molecular architecture.

(4)

and Lg =

l z

(5)

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where l ≅ 5 Å is the constant contour length per backbone monomer. Figure 5 shows ne,bb/ne,lin plotted versus dsc/Lg, which emphasizes the limiting behavior of graft polymers in the brush (dsc/Lg > 1) and comb (dsc/Lg < 1) limits. It is clear that two distinct regimes appear, differentiated by a sharp transition

ASSOCIATED CONTENT

S Supporting Information *

All primary data files are available at https://doi.org/10.13020/ D6T97M. The Supporting Information is available free of 528

DOI: 10.1021/acsmacrolett.8b00116 ACS Macro Lett. 2018, 7, 525−530

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ACS Macro Letters

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charge on the ACS Publications website at DOI: 10.1021/ acsmacrolett.8b00116. Experimental details, 1H NMR spectra, SEC traces, DSC thermograms, master plots, van Gurp-Palmen plots, reduced viscosity plots, and shift factors for all samples are included (PDF)

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AUTHOR INFORMATION

Corresponding Author

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

Ingrid N. Haugan: 0000-0002-8406-8939 Michael J. Maher: 0000-0003-0577-3726 Alice B. Chang: 0000-0001-5036-2681 Tzu-Pin Lin: 0000-0001-7041-7213 Robert H. Grubbs: 0000-0002-0057-7817 Marc A. Hillmyer: 0000-0001-8255-3853 Frank S. Bates: 0000-0003-3977-1278 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the NSF through the Center for Sustainable Polymers (CHE-1413862) and under award number CHE-1502616. This research used resources of the Advanced Photon Source (APS), a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Part of this work was performed at the DuPont−Northwestern−Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the APS. DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company, and Northwestern University.

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ACS Macro Letters

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DOI: 10.1021/acsmacrolett.8b00116 ACS Macro Lett. 2018, 7, 525−530