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Long-Chain Hyperbranched Comb Block Copolymers: Synthesis, Microstructure, Rheology, and Thermal Behavior Carlos R. Loṕ ez-Barroń ,* Patrick Brant, Maksim Shivokhin, Jiemin Lu, Shuhui Kang, Joseph A. Throckmorton, Trent Mouton, Truyen Pham, and Rebecca C. Savage ExxonMobil Chemical Company, Baytown, Texas 77520, United States

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S Supporting Information *

ABSTRACT: A series of poly(ethylene-co-acrylic acid)-cb-atactic polypropylene (EAA-cb-aPP) comb block copolymers were synthesized by grafting aPP-OH macromonomers onto a commercial EAA copolymer made by the high-pressure free radical process. The starting EAA copolymer contains 11 wt % of EAA units and has a significant amount of long chain branches. Therefore, the EAA-cb-aPP copolymers can be classified as hyperbranched. Room temperature atomic force microscopy and X-ray scattering measurements reveal strong, finely textured, phase segregation of the amorphous aPP and semicrystalline EAA domains, which persists in the melt state. The amorphous aPP side chains have an unexpected nucleating effect that facilitates crystallization of the EAA backbone, as evidenced by an increase in crystallization temperature. Moreover, phase segregation has a strong effect on both the linear and nonlinear viscoelastic response of the copolymers. Increases in both the branching density and branch chain length result in an improvement of melt strength as well as an increase in the extensional strain hardening (SH). We postulate that the SH enhancement may arise from the interfacial anchoring of the aPP side chains in the aPP homopolymer domains. This would produce additional resistance for the EAA backbone to stretch under uniaxial load due to an energetically unfavorable process of pulling the aPP arms into the EAA phase where they would face strong repulsions.



INTRODUCTION Despite the vast amount of studies devoted to the different aspects of polymers with block structure, their viscoelastic response has received very little attention. A typical test to characterize the order−disorder or order−order transitions (ODT or OOT) in block copolymers (BCP) is via dynamic temperature sweeps, where ODT and OOT are identified as sharp changes is the complex shear modulus.1−7 However, only a few attempts to establish relationships between microstructure and viscoelastic response of BCPs have been reported.8,9 Kossuth and co-workers8 proposed a “universal viscoelastic behavior” of block copolymers with cubic microstructure, consisting of a plateau in the elastic modulus, G′(ω) (denoted G0cubic). In entangled systems, this plateau occurs at considerably lower values of frequency and modulus than those characteristic of the rubbery plateau, G0N. In contrast, the low-frequency complex modulus of BCPs with lamellar and hexagonal phases have been observed to exhibit power law dependences G*(ω) ∝ (iω)α, with exponent α ≃ 0.5 for lamellar phases10−12 and α ≃ 0.3 for hexagonal phases.13 Note that most of the previous studies are on linear BCPs, whereas the rheological properties of block copolymers with different architectures (such as graft copolymers) are barely explored. Of particular interest for us are the poly(A-cb-B) comb blocks (also known as PA-g-PB graft copolymers). Recent studies have shown effective use of comb block (CB) copolymers as © XXXX American Chemical Society

compatibilizers of immiscible blends of A and B homopolymers14−19 and as rheology enhancers in blends with A homopolymers and in A/B immiscible blends.19,20 However, only a few studies on the viscoelastic response of CB copolymers have been reported to date.21−26 Stadler et al. reported creep and dynamic mechanical measurements of CB copolymers having polyethylene (PE) backbone and ethylene−propylene (EP) side chains (poly(PE-cb-EP)).23 They observed that the molecular weight−viscosity relation in these CB copolymers deviates significantly from the corresponding relations for linear and conventional long-chain branched (LCB) PEs. They explain this deviation based only on the branching architecture.23 However, they did not consider the possible phase segregation of the PE backbone from the EP side chains as a source of the unusual rheological response, although it is well-known that blends of PEs with different degrees of short branches do phase separate.27−30 Lin et al. studied the relations between melt microstructure and linear rheology of a series of poly(styrene-co4-(vinylphenyl)-1-butene)-g-polyethylene (PSVS-g-PE) copolymers with varying branching density.24 The found that low branching density resulted in microphase-separated structure and a rheological response typical of a network-like structures; Received: January 11, 2018 Revised: July 1, 2018

A

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by De la Fuente and co-workers in poly(tert-butyl acrylate-gstyrene) (PtBA-g-S) and poly(acrylic acid-g-styrene) (P(AA-g-S)) graft copolymers.21,22 Interestingly, the PSVS-g-PE samples with high branching density, studied by Lin et al.,25 presented homogeneous phase structure at high temperature and rheological behavior similar to linear or comb-like homopolymers.31−33 Note that the viscoelastic response of the P(AA-g-S) copolymers studied by De la Fuente et al.21 is strongly influenced by the presence of hydrogen bonds between the carboxylic acid groups that lead to an increase of backbone interactions. To our knowledge, all the previous rheological studies on CB copolymers have been focused on copolymers with linear backbones. In addition, only the linear shear rheology of such copolymers have been studied, although it is well-known that LCB has a profound effect on the extensional rheology of branched homopolymers.34 In this work, a series of hyperbranched EAA-cb-aPP comb block copolymers with poly(ethylene−acrylic acid) (EAA) branched backbone and atactic

Table 1. Properties of EAA GPC (g/mol × 1000)a,b

DSC

Tm, °C ΔHm, J/g wt % (mol %) AA Mn, kg/mol Mw, kg/mol Mz, kg/mol gw 95 75 11 (4.6) 29.3 211 1450 0.29 a

a

From grade specification sheet. bFor fully esterified derivative.

Table 2. Molecular Weights of the Side-Chain VT aPP Precursors and aPPOH Used in Grafting to EAAs, Measured by 1H NMR SC IDa

VT aPP

aPPOH

aPP1K aPP3K aPP7K

1223 2608 5720

1257 3319 6941

a

xK refers to approximate Mn (in kDa) of aPPOH.

i.e., a quasi-plateau in the plot of G′(ω) is observed in the lowfrequency regime. A similar rheological response was observed Scheme 1. Oxidative Hydroboration of VT aPP

Scheme 2. Esterification of EAA with aPP-OH

Figure 1. (a) DSC thermograms during cooling (upper panel) and heating (lower panel) for EAA and EAA-cb-aPP samples measured at 10 °C/min. (b) Crystallization and melting temperatures as functions of aPP wt % and aPP side-chain length schematic representation of the EAA/aPP interface. B

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Macromolecules Table 3. Properties of EAA and EAA-cb-aPP Copolymers crystallinity, % sample

Tg, °C

Tc, °C

Tm, °C

ΔHm, J/g

DSCa

WAXS

d, nm

DLT,b nm

DHT,b nm

EAA EAA-cb-aPP 1k-40 EAA-cb-aPP 3k-40 EAA-cb-aPP 7k-13 EAA-cb-aPP 7k-40 EAA-cb-aPP 7k-60

−16.9 −9.7 −3.8 −4.7 −5.9

72.1 71.3 71.6 77.1 74.4 71.5

96.5 90.3 92.9 95.3 95 92.8

56.9 32.6 36.9 46.7 37.4 30.8

19.4 11.1 12.6 15.9 12.8 10.5

20.8 13.3 13.1 15.7 12.5 9.43

13.9 11.0 12.1 11.0 13.5 14.2

16.1 18.9 48.3 39.2 25.1

∼35 ∼32 48.3 40.5 31.4

DSC crystallinity computed as ΔHm/ΔHPE, where ΔHEP is the heat of fusion for a 100% crystalline PE. bDLT = 2π/q**LT and DHT = 2π/q**HT are computed from maximum q**LT and q**HT values in the Kratky plots shown in Figures 6a and 6b, respectively. a

Figure 2. WAXS profiles of EAA and EAA-cb-aPP copolymers measured at 25 and 120 °C.



polypropylene (aPP) side chains were successfully synthesized via a “grafting to” approach of hydroxyl-terminated polypropylene macromers onto a commercial EAA copolymer. First we analyze the effect of aPP grafts on the thermal behavior and crystallinity of the copolymers in the solid state. We also study the melt microstructure via high-temperature small-angle X-ray scattering (SAXS), which correlates with the viscoelastic response to dynamic linear and extensional flows. Strong dependences of the rheological response on the aPP side chain length and aPP wt % are attributed to phase-segregated morphologies.

EXPERIMENTAL METHODS

Materials and Synthesis. A commercial ethylene acrylic acid (EAA) copolymer (Escor 5100) was provided by ExxonMobil and used as received. Selected properties of this high-pressure free radical produced autoclave copolymer are summarized in Table 1. The product is long chain branched, which is quantified by the low gw value of 0.29 (for its fully esterified derivative). This parameter is defined as the ratio between the root mean-square radius of gyration of the sample (measured with the light scattering detector of the GPC instrument) to that of its linear counterpart having the same molecular mass.35 Preparation of Hydroxyl-Terminated Atactic Polypropylene. Three atactic polypropylene macromonomers (VT aPP, 95+% of C

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Macromolecules chains allyl terminated) were prepared in a 2 L stainless steel reactor as described previously.36,37 Their number-average molecular weights are given in Table 2. Conversion of the VT aPPs to hydroxyl-terminated aPP (depicted in Scheme 1) was carried out following a procedure similar to that described by Dalsin et al.38 Details of the synthesis can be found in the Supporting Information. The 1H NMR spectrum of an allyl-terminated aPP and the corresponding aPP-OH products are shown in Figures S1 and S2, respectively, and their molecular weights are listed in Table 2. Esterification of EAA with aPP-OH. The aPP side chains were grafted to the branched EAA copolymer via esterification reactions carried out under nitrogen in refluxing xylene with p-toluenesulfonic acid (p-TsOH) catalyst. Reaction time was 24 h in all cases (see Scheme 2). Typical total mass of EAA and atactic polypropylene combined in each reaction was maintained at 4 g, and the total p-TsOH was 40 mg (0.23 mmol). Water was collected in a Dean−Stark trap. All products were dried in vacuo at 50 °C for several hours. Conversion to desired ester was determined by 1H NMR using the following conditions: 20 mg of product was dissolved in TCE-d2, and the spectrum was recorded at 130 °C. The comb block products are named EAA-cb-aPP Xk-Y, where X is the nominal molecular weight of the aPP side chain (in line with the nomenclature in Table 2) and Y is the wt % of aPP arms, as determined by NMR. Given that the aPP grafts are simply linear chains, these provide and additional level of branching to the LCB topological structure of the EAA copolymers. Differential scanning calorimetry (DSC) of the copolymers was carried out using a DSC Q100 (TA Instruments) with a heating rate of 10 °C/min. GPC traces of the EAA and EAA-cb-aPP 3k-40 copolymers are given in the Supporting Information. Because of the well-known technical issues associated with strong interactions between nonfully esterified EAA copolymers and the GPC columns, we were not able to measure GPC data on all the samples. However, the GPC provided on the selected sample show a noticeable decrease in branching index (g′), indicative of successful grafting. NMR spectra before and after esterification are shown in the Supporting Information. The NMR plots show substantial attachment of aPPOH to EAA via esterification; signal integration, with comparison to starting aPPOH, suggests virtually quantitative conversion to ester. However, the “end group” signals are inherently weak so having a small amount of not attached aPP is probable. Rheological Measurements. Plaques of the copolymers with 0.5 mm thickness were molded in a hot press at 150 °C and subsequently cut into 8 mm discs and 12.7 mm × 20 mm rectangles for shear and extensional rheology, respectively. These molded plaques were also used for X-ray scattering and AFM measurements. Dynamic frequency sweeps (DFS) measurements were performed at temperatures ranging from 90 to 210 °C, using a strain-controlled ARES-G2 rheometer (TA Instruments) with (8 mm) parallel plate geometry and strain amplitude of 10%. The frequency range used for the DFS measurements at each temperature was 100 to 0.01 Hz. All measurements were carried out under nitrogen purge to minimize sample degradation. Extensional rheology was measured at 120 °C using a Sentmanat extensional rheometer (SER)39 attached to a stress-controlled DHR rheometer (TA Instruments). These measurements were conducted at four Hencky strain rates (ε̇H): 0.01, 0.1, 1.0, and 10 s−1. X-ray Scattering Measurements. Small- and wide-angle X-ray scattering (SAXS and WAXS) measurements were performed on a SAXSLAB Ganesha 300XL+ instrument equipped with a Xenocs GeniX high brilliance microfocus sealed tube X-ray source (energy = 8 keV, Cu K, λ = 1.54 Å), focusing optics, and Dectris Pilatus 300K detector (487 × 619 pixels, pixel dimension 172 μm). Data processing was performed with the computer program SAXSGUI (JJ X-ray Systems ApS and Rigaku IT, Inc.). Distances were calibrated using silver behenate. The scattering patterns were normalized to the primary beam intensity and corrected for background scattering. The measurements were carried out at 25 and 120 °C using a Linkam Testing Stage model TST350 (Linkam), where the temperature of the samples was equilibrated for 10 min before the measurements. Atomic Force Microscopy. Morphologies of the comb block copolymers were examined using a bimodal AFM (Cypher, Asylum Research) after cryo-facing using a cryo-microtome (Leica) at −120 °C.

Figure 3. (a) WAXS peak analysis. WAXS data, measured at 25 °C, was fitted with two amorphous Gaussian peaks and three crystalline Gaussian peaks. The cumulative fit is the sum of amorphous and crystalline peaks. (b) Crystallinity as a function of aPP wt % for the EAA-cb-aPP copolymers.



RESULTS AND DISCUSSION Thermal Behavior and Crystallinity. The neat EAA is a semicrystalline polymer with melting peak (Tm) located at 96.5 °C and onset of crystallization (Tc) at 76 °C. As expected, grafting of the amorphous aPP chains onto the EAA backbone alters the crystallinity and melting behavior of the copolymers. The DSC thermograms of the EAA and the EAA-cb-aPP copolymers are displayed in Figure 1, and the glass transition, melting, and crystallization temperatures (Tg, Tm, and Tm, respectively) as well as the heat of melting are listed in Table 3. Grafting to the EAA backbone produces the expected effect on the glass transition of the aPP side chains; namely, the Tg are shifted to higher values which are closer to those of the aPP-OH (−8.6 °C for aPP-OH 1k and 0 °C for aPP-OH 3k and 7k). Another expected effect is that grafting of the amorphous aPP side chains produces a decrease in the melting temperature, which, as shown in Figure 1b, is a decreasing function of the aPP content. An unexpected behavior is that the crystallization temperatures of samples EAA-cb-aPP 7k-13 and EAA-cb-aPP 7k-40 are higher than the neat EAA and decrease as the aPP content increases, as shown in Figure 1b. We speculate that this unexpected increase in Tc is due to a nucleating effect of the EAA crystals occurring at the interphase between the aPP and the EAA domains (phase segregation is discussed in the next section): segments of the EAA chains that are attached to the aPP side chains lie perpendicular to the EAA/aPP interface (as illustrated by the schematic cartoon in Figure 1b), and therefore they are more prone to crystallize than the EAA segments in the bulk of the EAA phase. This effect is stronger for longer aPP side chains and competes with the effect of increasing the amorphous (aPP) content in the system D

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Figure 4. SAXS profiles of EAA and EAA-cb-aPP copolymers measured at 25 and 120 °C.

(which decreases Tm values). A similar nucleating effect was observed by Wang et al. in polypropylene-g-poly(ethylene-co-1butene) (PP-g-EB) graft copolymers.26 However, in those polymers the EB side chains are miscible with the PP backbone; therefore, the mechanism of nucleation is fundamentally different. The heat of fusion due to the melting of the EAA crystals (ΔHm) is a decreasing function of the aPP content in the copolymer. This indicates that the overall crystallinity decreases with increasing aPP branching content, as confirmed by the X-ray diffraction measurements. Indeed, the crystallinity values computed as crystallinity = ΔHm/ΔHPE (based on ΔHPE = 290 J/g for a 100% crystalline PE)40,41 are very close to those computed from WAXS data (see Table 3). Figure 2 shows WAXS data for the EAA and selected EAA-cbaPP copolymers measured at 25 and at 120 °C. WAXS profiles measured at room temperature consist of an isotropic halo and four diffraction peaks at q values: 1.51, 1.66, 2.08, and 2.51 Å−1. The first two peaks are the (110) and (200) reflection peaks (see Figure 3a) related to the orthorhombic crystal structure of the EAA backbones, which is similar to that observed in polyethylene.42 The crystallinity is computed by integration of the amorphous peak and the orthorhombic crystalline peaks, as illustrated in Figure 3a for the sample EAA-cb-aPP 7k-40 (WAXS peak analysis of the rest of the samples is shown in

Figure S5). Note that two Gaussian peaks are used to accurately fit the amorphous peak, whereas one Gaussian peak was used to fit each of the crystalline peaks. The ratio of the integrated intensity under the crystalline peaks to the integrated intensity under the complete WAXS diffraction trace yields the degree of crystallinity (tabulated in Table 3). Figure 3b shows the expected decrease in crystallinity with increasing aPP content in the copolymer. Microstructure in the Semicrystalline and Melt States. The bulk morphology of the comb block copolymers was characterized by AFM and SAXS measurements at room temperature and at high temperature (T > Tm) only by SAXS. Figure 4 shows the SAXS profiles for the EAA and selected EAA-cb-aPP copolymers. At 25 °C a broad peak centered at a q value of q* = 0.045 Å−1 is observed for the EAA copolymer, which correspond to an average lamellar distance (computed as d = 2π/q*) of 13.9 nm. This peak is also present in the SAXS profiles for the EAA-cb-aPP copolymers, which indicates that the orthorhombic crystals formed by the EAA backbone in the comb block copolymers arrange in the same type of chain-folded lamellar structure with similar d-spacing. An additional feature in the SAXS profiles of the EAA-cb-aPP copolymers, not observed in the neat EAA copolymer, is a peak (or shoulder) at q values lower than q*. This additional peak arises from segregation of the aPP side-chain blocks from the EAA backbone chains. E

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Figure 5. AFM micrograph at 25 °C for sample EAA-cb-aPP 7k-40. Dark regions are crystalline (hard) domains, and bright regions are amorphous (soft) domains.

Such phase segregation is evident in the AFM micrographs shown in Figure 5. An AFM micrograph of the neat EAA copolymer, given in the Supporting Information, shows the lamellar structure with repeat distance in the order of 10 nm and shows no sign of phase segregation. To verify that the low-q SAXS peaks are due to phase segregation, and not related to the EAA crystalline structure, SAXS and WAXS measurements were performed at 120 °C (data shown in Figures 2 and 4). The full disappearance of the orthorhombic peaks in the WAXS profiles confirms complete melting at 120 °C. By comparing the SAXS profiles measured at low temperature with those measured at high temperature, it is clear that upon melting only the EAA (long distance) lamellar peaks disappear, whereas the low q peaks remain in the melt state. This is clearer in the Katky plots (plots of I(q)·q2 vs q) presented in Figure 6. This confirms that the SAXS peaks observed at 25 and 120 °C, centered in the q values q**LT and q**HT (as indicated in Figure 6), respectively, arise from phase segregation in the melt, which is key to understand the linear and nonlinear viscoelastic response of the comb block copolymers, as discussed below. The interdomain distances DLT = 2π/q**LT and DHT = 2π/q**HT, given in Table 3, are decreasing functions of the aPP content. Note that scattering arising from domain segregation consist of a single broad peaks with no higher-order peaks, which indicates that the segregated phases form disordered domains, as evidence in the AFM micrograph shown in Figure 5. This is not unexpected, given that the starting EAA copolymer has large polydispersity and LCB architecture, which highly restrict the probability for the aPP domains to arrange in ordered phases. Linear Viscoelasticity. Dynamic master curves of the elastic and viscous moduli (G′ and G″, respectively) of EAA and EAAcb-aPP copolymers are shown in Figure 7. It is worth noting that the dynamic master curves of the EAA copolymer show the typical shape of a branched polymer, despite the presence of 4.6 mol % AA groups in the backbone. This is more evident by

Figure 6. Kratky representation of the SAXS data for the EAA and EAA-cb-aPP copolymers measured at 25 and 120 °C.

analysis of the van Gurp−Palmen plot of phase angle (δ) versus complex modulus (shown in Figure S7), which shows the double shoulder shape for the EAA copolymer that is typical of long-chain branched polymers.43 As discussed elsewhere, hydrogen bonds formed between carboxylic acid groups in AA-containing copolymers could lead to strong backbone association which strongly influence the terminal relaxation.21,44 Dong and co-workers45 described the coexistence of various types of hydrogen forms in PAA homopolymers and the fact that these different structures of hydrogen bonds persisted even when the temperature rose well above the Tg. Apparently, the amount of AA groups in our EAA copolymer is too low to show signs of H-bonding effects in the viscoelastic response. Most of the samples (except for the EAA-cb-aPP 7k-60 copolymer) obey the time−temperature superposition (tTs) principle in the temperature range studied. The temperature dependence of the time and modulus shift factors (aT and bT) used to construct the master curves are shown in Figure 8. The solid lines are fits to the Williams−Landel−Ferry (WLF) equation (log aT = −C1(T − Tr)/[C2 + (T − Tr)]), using the parameters C1 and C2 listed in Table 4. Failure of the tTs principle for the EAA-cb-aPP 7k-60 copolymer is not unexpected as this sample has the strongest segregation among all the samples. The relaxation of the network formed by the interconnected domains is not expected to have the same temperature dependence as the EAA backbone and the aPP side chains, which is a F

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Figure 7. Master curves of dynamic moduli for the EAA and EAA-cb-aPP copolymers constructed via tTS with a reference temperature T0 = 120 °C. Data for the EAA copolymer are included in all the plots (gray symbols) for comparison.

properties that translate into good melt processability. Another highly advantageous rheological property is extensional strain hardening, which is discussed in the next section. The viscoelastic response of the EAA-cb-aPP 1k-40 seems to indicate that grafting very short aPP chains onto the EAA backbone has a simple plasticizing effect, in which the dynamic moduli and complex viscosity curves are shifted to lower values than those for EAA. This effect is intriguing, however not well understood by the authors, given that similar to the rest of the comb block copolymers, this sample shows phase segregation in the melt. For the rest of the comb block copolymers, an increase in the moduli and viscosity with respect to the EAA copolymer are observed. The increase in those parameters are functions of both the length of the grafted aPP side chains (Lsc) and the degree of grafting (aPP wt %). Note that although the terminal regime (where the dynamic moduli have the power law dependences with frequency: G′ ∝ ω2 and G″ ∝ ω) could not be reached for most of the comb block copolymers, an increase in the power law exponent is evident, as indicated in Figure 7. As expected, this effect is stronger in the sample with the longest side chains and the

requirement for tTs principle to be obeyed. Indeed, what is surprising is that the rest of the samples obey this principle, given their heterogeneous microstructure. The reason for this is not well understood; however, this behavior has been recently reported in other copolymers with comb block architecture.21,22,24 The dynamic moduli (Figure 7) and the complex viscosity (Figure 9) for all the comb block samples show lower values in the high-frequency regimes than the EAA copolymer. This indicates that grafting aPP improves the frequency dependence of the complex viscosity (except for the EAA-cb-aPP 1k-40). This response could be indication of enhanced shear thinning, assuming that the Cox−Merz rule is obeyed by our samples. Unfortunately, we did not synthesize enough sample volumes to measure steady shear viscosity (using capillary rheology) and to verify the Cox−Merz rule. Additional rheological enhancement due to aPP grafting is the increase in melt strength, which is evinced in Figure 9 by the increase in zero-shear viscosity, η0, for most of the comb block copolymers (except for the EAA-cb-aPP 1k-40), compared to the value for the neat EAA copolymer. Both shear thinning and melt strength are desirable rheological G

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Figure 8. Time and modulus shift factors as a function of temperature, calculated via tTs principle, with a reference temperature T0 = 120 °C. Solid lines are best fits to the WLF equation using the parameters C1 and C2 listed in Table 4.

Table 4. Rheological Parameters of EAA and EAA-cb-aPP Copolymers sample

C1

C2, °C

EAA EAA-cb-aPP 1k-40 EAA-cb-aPP 3k-40 EAA-cb-aPP 7k-13 EAA-cb-aPP 7k-40 EAA-cb-aPP 7k-60

8.94 6.84 3.56 5.63 8.05

295 240 110 181 209

greater aPP content, namely, EAA-cb-aPP 7k-60 sample. On this sample a clear elastic plateau modulus is observed at low frequencies, indicating solid-like behavior. This is due to the very strong block segregations and the “network” structure in the melt, which in turn results on the strongest extensional strainhardening effect, as discussed below. Extensional Rheology. We now discuss the nonlinear viscoelastic response to uniaxial extension. Figure 10 shows the transient extensional viscosity for all the EAA and EAA-cb-aPP copolymers measured at 120 °C (well above the Tm of all the samples) using four Hencky strain rates. The solid lines in Figure 10 are linear viscoelastic envelop (LVE) predictions using the DFS data shown in Figure 7. These data are first fitted to the discrete relaxation spectra N

G′(ω) =

∑ gi i=1

at ε > 1 strong strain hardening (SH) is observed in all the samples, including the EAA copolymer. Strain hardening manifests as an upward growth of the stress component in the direction of flow away from the LVE prediction. The observation of SH in the EAA sample is not unexpected, as this copolymer contains long chain branches, which are known to produce strong SH.34,46,47 The enhanced SH observed in branched polymers results from the exponential increase of relaxation times, which generates additional elasticity in response to strong extensional flow.48 The molecular mechanism responsible for this phenomenon is thought to be related to a strong suppression of the chain reptation (where reconfiguration can only be achieved by hierarchical arm retraction), which is exponentially slower compared to analogous (i.e., of same molecular weight) linear chains.49 Most of the EAA-cb-aPP copolymers show stronger SH than the neat EAA copolymer (Figure 10). To quantify the strength of SH, we compute the strain hardening ratio, measured at a Hencky strain of 3, as the ratio between the measured extensional viscosity and the viscosity obtained from the LVE prediction: SHR(ε = 3) = η+E(ε = 3)/3η+(ε = 3). Figure 11 shows the SHR values for all the EAA and EAA-cb-aPP copolymers, measured at the four strain rates studied here. An increase in the SHR with strain rate is observed for all the samples. Figure 11a

(ωλi)2 1 + (ωλi)2

N

G″(ω) =

Figure 9. Complex viscosity versus frequency for the EAA and EAA-cbaPP copolymers grouped as (a) varying side chain length and (b) varying aPP content.

∑ gi i=1

ωλi 1 + (ωλi)2

(1)

with the parameters gi and λi given in Table S3, which are used to compute the LVE extensional viscosity as N

ηE+,LVE(t )

+

= 3η (t ) = 3 ∑ giλi(1 − exp(−t /λi) i=1

(2)

Figure 10 shows that the extensional viscosity data, for all the samples, at all strain rates studied, align well with the LVE predictions up to Hencky strain values of ε = ε̇t ∼ 1. However, H

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Figure 10. Transient extensional viscosity for the EAA and EAA-cb-aPP copolymers measured at 120 °C at the indicated strain rates. Solid lines are LVE calculations.

have an increasing effect on the elasticity and the nonlinear response in entangled polymers. However, this effect should not be significant given that the aPP side chains are unentangled (the entanglement MW for aPP is ∼5.7 kg/mol),50 and therefore they do not provide additional entanglement to the copolymers. Deconvolution of these two effects is not straightforward and beyond the scope of this work; however, further investigation in this direction is warranted. To rationalize the trends observed in Figure 11, one may argue that increase in both aPP length and content in the copolymers produces stronger segregation by producing stronger anchor points (if the aPP side chain length increases) or more anchors (if wt % of aPP increases) in the aPP domains. Those anchor points would produce additional resistance for the EAA backbone to stretch under uniaxial load, since (as illustrated in Figure 12) such stretching would involve an energetically unfavorable process of pulling the aPP arms into the EAA phase where they would face strong repulsions. Strong resistance to such processes manifests as enhanced extensional strain hardening, as evidenced in Figures 10 and 11.

(which includes samples EAA-cb-aPP 1k-40, EAA-cb-aPP 3k-40, and EAA-cb-aPP 7k-40) shows a monotonic increase in SH with side chain length at all rates. Note that the SHR values for the EAA-cb-aPP 1k-40 are slightly lower those for the EAA copolymers, which correlates well with the lower melt strength (lower zero-shear viscosity) observed in the comb block copolymers (see Figure 9a). Figure 11b (which includes samples EAA-cb-aPP 7k-13, EAA-cb-aPP 7k-40, and EAA-cb-aPP 7k-60) shows that SHR also increase with increasing grafting (aPP wt %), with a sharp increase when the grafting jumps from 40 to 60%. We speculate that the nontrivial increase in SHR observed in the comb block copolymers, compared to the neat EAA copolymer, is mainly due to the extra elasticity produced by the phase segregation of the aPP side chains from EAA domains, which is evident by the increase in G′ in the low-frequency regime of the DFS curves (Figure 7). Note that EAA-cb-aPP 1k-40 shows no elasticity increase and therefore no SH improvement. It should be noticed that phase segregation may not be the only contribution to the extra SH, since grafting of the aPP side chains also increase the overall level of branching, which is known to I

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Article

Macromolecules

comb block copolymers with varying aPP side chain length and content. These polymers were prepared by grafting aPP macromers onto a commercial LCB EAA backbone via oxidative hydroboration of vinyl-terminated aPP followed by esterification with EAA. As expected, the orthorhombic crystallinity of the EAA backbone decreases with increasing amorphous aPP graft content. An unexpected observation is an increase in Tc with low grafting level of the aPP macromers. This suggests that even though the aPP side chains are amorphous, they act as crystal nucleators due to an entropic constraint effect acting on the EAA chain segments close to the EAA/aPP interphase. Segregation of EAA and aPP domains is observed in all the EAAcb-aPP copolymers both in the solid state and in the melt. This segregation has profound effects on the viscoelastic response of the copolymers. In general, stronger frequency dependence of the complex viscosity and enhanced melt strength result from increasing both aPP side chain length and aPP graft content. Because of the LCB architecture of the commercial EAA, this polymer displays nontrivial extensional SH, which is further increased by grafting aPP macromers onto the EAA backbone. We postulate that this increase in SH is due to the anchoring of the aPP side chains into the phase-segregated aPP domains, which in turns produces resistance for the EAA backbone to stretch under extensional deformation.



ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00068.



Figures S1−S11 and Tables S1−S3 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (C.R.L.-B.). ORCID Figure 11. Strain hardening ratio as a function of (a) aPP side chain length and (b) aPP wt % for all the EAA and EAA-cb-aPP copolymers. Data in (a) includes samples EAA, EAA-cb-aPP 1k-40, EAA-cb-aPP 3k-40, and EAA-cb-aPP 7k-40, whereas data in (b) includes samples EAA, EAA-cb-aPP 7k-13, EAA-cb-aPP 7k-40, and EAA-cb-aPP 7k-60. Measurements were carried out at 120 °C at the indicated strain rates.

Carlos R. López-Barrón: 0000-0002-9620-0298 Maksim Shivokhin: 0000-0003-3725-9959 Notes

The authors declare no competing financial interest.



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Figure 12. Schematic illustration of the stretching process of EAA-cbaPP copolymer during uniaxial extension (arrows indicate the direction of stretching).



CONCLUSIONS We present the thermal behavior, the microstructure, and the rheological response of a series of hyperbranched EAA-cb-aPP J

DOI: 10.1021/acs.macromol.8b00068 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b00068 Macromolecules XXXX, XXX, XXX−XXX