Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Molecular Dynamics of Polyfarnesene Ciprian Iacob,*,†,‡ Taejun Yoo,§ and James Runt*,† †
Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ National Research and Development Institute for Cryogenic and Isotopic Technologies, ICSI, 240050 Râmnicu Valcea, Romania § Total Petrochemicals & Refining USA, Inc., Total Cray Valley, 665 Stockton Drive, Suite 100, Exton, Pennsylvania 19341, United States Downloaded via UNIV OF TOLEDO on June 29, 2018 at 13:54:03 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: This paper represents the first comprehensive report of the molecular weight dependence of the dynamics of polyfarnesene (PF), utilizing oscillatory shear rheology and broadband dielectric spectroscopy. Extended PF chain conformations arising from tightly packed C11/C13 pendant groups reduce the probability of chain entanglements and lead to Rouse-like melt dynamics up to a critical molecular weight ∼105 g/mol. At higher molecular weights, PF behaves as an entangled polymer melt. Dielectric spectroscopy measurements establish PF as a type-A polymer, whose normal mode relaxation is strongly dependent on molecular weight, providing a compliment to melt rheology for the exploration of PF global chain dynamics.
Scheme 1. Polyfarnesenea
1. INTRODUCTION Along with the rapid natural gas feedstock growth in support of chemical manufacturing, interest in creating chemicals and polymers from renewal biological sources has continued and grown in popularity. One such biobased molecule is trans-βfarnesene (7,11-dimethyl-3-methylene-1,6,10-dodecatriene), produced by yeast fermentation of sugar feedstocks.1,2 βFarnesene possesses an anionically polymerizable conjugated diene structure, and synthesis of linear backbone polyfarnesene (PF) oligomers and polymers with narrow-molecular-weight distributions has been demonstrated in a recent publication, along with selected PF properties.2 PFs are noncrystalline, exhibit rather low glass-transition temperatures (∼197 K), and have relatively low melt viscosities (very much less than polybutadiane when compared at the same molecular weights2). As seen in Scheme 1 and discussed later, the repeating unit structure of the PFs under investigation consists of two or four carbon atoms in individual backbone units and considerably longer C11 or C13 pendant groups. The pendant groups are densely packed, and at higher molecular weight the chains are expected to be bottlebrush-like,3−7 with the tightly spaced side chains encouraging the polymer to adopt a cylindrical bottlebrush structure with large persistence length, arising from excluded volume effects. An additional intriguing feature of polyfarnesene is that the backbone segments are analogous to isoprene. (β-farnesene can be thought of an isoprene trimer.) Like cis- (and trans-) 1,4-polyisoprene (PI)8−10 and a modest number of other polymers,11−13 in addition to having a component of the repeating unit dipole moment perpendicular © XXXX American Chemical Society
a
Consisting primarily of 1,4-(cis, trans)-addition products (C11 pendant groups) and ∼10 mol % 3,4-addition products (C13 pendant units).
to the chain, there is a cumulative dipole moment parallel to the chain contour (i.e., repeat units do not have a plane of symmetry and are so-called type-A polymers). The chain can be relaxed by what is known as the dielectric normal mode, reflecting the fluctuation of the end-to-end vector characterizing the global chain dynamics. Consequently, for type-A polymers, broadband dielectric spectroscopy (BDS) facilitates the exploration of local, segmental, and longer whole-chain dynamics in the same experiment. This paper represents the first comprehensive report of the dynamics of PF utilizing both oscillatory rheology and BDS. Received: April 22, 2018 Revised: June 11, 2018
A
DOI: 10.1021/acs.macromol.8b00851 Macromolecules XXXX, XXX, XXX−XXX
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SEC traces of each PF versus absolute Mw are displayed in Figure 1b. Table 1 provides a summary of the characteristics of all of the PFs
2. EXPERIMENTAL SECTION Purified trans-β-farnesene (High Performance BioFene, Amyris) was anionically polymerized in heptanes using n-butyl lithium as the initiator, as described in more detail in ref 2. The PFs under investigation in this study were acid-neutralized (leading to nonfunctional end groups), and the resulting lithium salts were filtered prior to solvent removal via steam stripping (under N2). This synthetic procedure leads to a chain microstructure composed of primarily 1,4-(cis, trans)-addition products (i.e., C11 pendant groups) and ∼10 mol % 3,4-addition products (C13 pendant units), as determined from 1H NMR.2 No 1,2-addition products were detected using Fourier transform infrared spectroscopy.2 Size exclusion chromatography (SEC) of all samples (Figure 1) was conducted using a Tosoh EcoSEC instrument. Dilute solutions of PF
Table 1. Weight-Average Molecular Weights, Polydispersity Indices, and Glass-Transition Temperatures from DSC and Rheological Measurements (LVE) sample ID
Mw (g/mol)
PI
TgDSC (K)
TgLVE (K)
PF3.8K PF5.8K PF7.2K PF9.4K PF36.7K PF64K PF176K PF225K PF367K
3800 5800 7200 9400 36 700 64 000 176 200 225 400 367100
1.15 1.11 1.10 1.15 1.28 1.29 1.23 1.27 1.18
192 196 198 199 197 198 198 200 200
192 194 197 198 197 197 195 198 198
explored in the present investigation. Mw ranges over nearly two orders of magnitude from 3.8 to 367 kg/mol, and all polymers have relatively narrow molecular-weight distributions (PI = Mw/Mn = 1.1 to 1.29). Oscillatory shear measurements were performed on a straincontrolled Rheometrics Advanced Rheometric Expansion System rheometer (TA Instruments) with a force rebalance transducer measuring 2 μN m to 200 mN m torque. All PFs were dried under vacuum at 373 K for 12 h to remove water and then loaded onto parallel plates with diameter of 8 and 3 mm for the acquisition of storage and loss moduli (G′ and G′′) isotherms, measured over a frequency range of 100−0.1 rad s−1 under a nitrogen atmosphere. The strain amplitude was selected to be within the linear viscoelastic range. The measured G* for each temperature (ranging from 218−395 K) was then reduced at a reference temperature of 293 K (∼Tg + 93K) to form the respective master curves. Glass-transition temperatures from LVE (Tg,LVE, see Table 1) were obtained at the transition in the shift factors from WLF to Arrhenius behavior15 and are identical to those determined from DSC within experimental uncertainty. Dielectric spectroscopy measurements were conducted over a broad frequency range (0.1 Hz to 10 MHz) and temperature interval (120−400 K) utilizing a Novocontrol Concept 40 high-resolution alpha dielectric analyzer. A Quatro temperature controller was employed using pure nitrogen as a heating agent and provided temperature stability better than 0.2 K. The measurements were conducted using platinum electrodes in a parallel plate capacitor configuration. All sample preparation was conducted in a glovebox to avoid water uptake, and prior to the measurements, the samples were dried at 373 K for 12 h in a vacuum oven. The PFs under study exhibit relatively low impurity conductivity at temperatures above (frequencies below) the segmental α process. The dielectric α and normal mode (n) processes are relatively well separated even for lowmolecular-weight variants (Figure 2) and are resolved by fitting two Havriliak−Negami (HN) functions to the two relaxation processes.16 The empirical HN extension of the Debye model is
Figure 1. (a) Specific refractive index increment versus absolute weight-average molecular weights and (b) SEC traces for all PF samples versus the absolute Mw. in tetrahydrofuran (THF) were analyzed in a THF mobile phase at 40 °C at a concentration of ∼2 mg/mL. Prior to these measurements, the PF solutions were filtered two times through a 0.2 μm PVDF membrane. Absolute weight-average molecular weights (Mw) were determined using a Wyatt Dawn Heleos-II 8 light scattering detector. The differential refractive index (dn/dc) values for each PF polymer in THF at different concentrations of 1.0, 1.5, 2.0, 3.0, 4.0, and 5.0 mL/g were determined at 40 °C by using a Brookhaven differential refractometer operating in static mode with a laser source at 620 nm. The differential refractive indices for all PFs under investigation are plotted in Figure 1. In general, dn/dc has been shown to increase a few percent with increasing molecular weight up to ∼10 000 to ∼20 000 g/mol, depending on the solvent, polymer shape, and endgroup contributions to the refractive index.14 Above this range it remains constant. This is consistent with the PF data in Figure 1a, where the dn/dc increases from 0.135 for PF3.8K to 0.143 for PF9.4K and remains constant for the remaining higher molecular weights polymers.
* = εHN
Δε [1 + (iω /ωHN)a ]b
where Δε is the relaxation strength, a is a fitting parameter that is inversely related to the breadth of the relaxation, b is the highfrequency asymmetry parameter, and ωHN is a characteristic frequency related to the frequency of maximum loss ωmax by i aπ yz zz ωmax = ωHNjjjsin k 2 + 2b {
1/ a
ij abπ yz jjsin zz k 2 + 2b {
−1/ a
Figure 2 shows the typical dielectric spectra of PF3.8K. Three relaxation processes are observed. The relaxation at lower frequencies is attributed to the normal mode relaxation (n), and the stronger process at higher frequencies is the segmental relaxation process (α). B
DOI: 10.1021/acs.macromol.8b00851 Macromolecules XXXX, XXX, XXX−XXX
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to Arrhenius dependence associated with the monomer relaxation. The reduced complex viscosities versus reduced frequency for all PFs are displayed in Figure 4 (Tref = 293 K). The
Figure 2. PF3.8K dielectric loss spectra at selected temperatures as a function of frequency. Three relaxation processes are observed: the normal mode (n), α relaxation, and β relaxation. On the high-frequency side of the α process, an additional relaxation (β) is observed and attributed to a local relaxation in the glassy state.
Figure 4. Reduced complex viscosity versus reduced frequency for the PFs studied herein at a reference temperature of 293 K. Inset: A zoom-in is presented for clarity.
3. RESULTS AND DISCUSSION 3.1. Oscillatory Shear Rheology. Master curves were constructed for all PFs: Those for PF367K are displayed in Figure 3, and all others are shown in Figure 1 along with the corresponding Williams−Landel−Ferry (WLF) shift factors (aT). The frequency shift factors between 393 and 198 K for PF367K (inset in Figure 3) are well fitted by the WLF equation. The deviation between the WLF fit and the experimental data is observed at the glass-transition temperature (Tg = 198 K) when the shift factors transition from WLF
measured zero shear viscosities (η0) are displayed in Figure 5 as a function of Mw at 293 K (∼Tg + 93K). For flexible linear polymers, η0 is well known to depend on M1 below and on M3.4 above, a polymer-specific critical M (Mc, where Mc ≈ 2Me, the entanglement molecular weight).17 As seen in Figure 5, the
Figure 5. Open symbols: Zero shear viscosities at 293 K (∼Tg + 93 K) as a function of Mw for the polyfarnesene series. Mw is used because the terminal mode is dominated by the longest chains. Solid colored symbols: Relaxation times for the PF dielectric normal mode at 293 K. Crossed gray symbols are the data from the literature of the PI for the dielectric normal mode under an isofriction condition (τn/ τα): crossed triangles (Imanishi et al.19), crossed circles (Adachi et al.20), crossed squares (Matsumiya et al.21), and crossed diamond (Sato et al.22). Inset: Dielectric normal mode relaxation times for PFs as a function of Mw at an isofrictional state. The dotted vertical lines represent the approximate Mc for PI and PF. Slope values are also indicated.
Figure 3. Master curves at 293 K for storage and loss moduli of PF367K spanning from the terminal region to the glassy state (as indicated). Inset: Frequency shift factors (aT) used to generate the master curves. The WLF equation is log(aT) = C(Tr − T)/T − T∞), where Tr is the reference temperature (293 K), C is an empirical fitting parameter (8.4), and T∞ is the Vogel temperature where the free volume is zero (152 K). C
DOI: 10.1021/acs.macromol.8b00851 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules polyfarnesenes display a clear transition in the slope of log η0 versus log Mw to ∼3.1±0.3 at higher molecular weights, indicative of the transition to entangled chain dynamics. The presence of entanglements at higher M is verified by the presence of a rubbery plateau and crossover in G′ and G′′,17 as displayed in the representative master curve for PF367K in Figure 3. Below Mc, there is no indication of G′/G′′ crossovers nor a plateau modulus. (See the comparison between the master curves for PF64K and PF367K in Figure 6 as well as
ments, and, given the chemical architecture of the PFs and the similarity with the findings in ref 22, we conclude that PFs with Mw ≤ 105 g/mol behave like bottlebrush polymers. The fact that increasing pendant lengths increase Me is supported by previous research on polymyrcene (poly(1,6-octadiene-7methyl-3-methylene)) which has similar isoprene-like repeat unit chemistry but with densely packed C6 branches. The molecular weight between entanglements for polymyrcene has been reported to be 18 000 g/mol (Mc ≈ 36 000 g/mol),26 between those of linear PI and C11/C13 pendant PF. 3.2. Dielectric Spectroscopy. One way of viewing the general features of the dielectric spectra of the PF family of materials is seen in Figure 7: the isochronal dielectric loss at 1.2 kHz. Three processes are clearly observed, and their relaxation maps are displayed in Figure 9.
Figure 6. Comparison of dynamic master curves of G′ and G′′ for PF64K and PF367K at a reference temperature of 293 K. Data for PF367K are vertically shifted by a factor of 106.
Figure S.1) Rheology data from Figure 3 allow us to measure the value of the molecular weight of entanglement Me by measuring G0n, the value of G′ around the middle of the elastic plateau that corresponds to the minimum of tan δ. According to Doi and Edwards18
Figure 7. Isochronal plots of dielectric loss versus temperature at 1.2 kHz for PFs having Mw ranging from 3.8K to 367K g/mol. Individual loss spectra are identified in the legend at the bottom of the Figure, with Mw increasing from top to bottom. Spectra are offset vertically (as indicated) for clarity.
Me = ρRT /Gn0
where ρ = 0.9 g/cm3 is the density (determined at room temperature using a high-precision helium pycnometer AccuPyc II 1340 (Micrometrics Instrument Corporation); see Table S2), R = 8.32 J K−1 mol−1 is the ideal gas constant, and T is the temperature of the measurement. By using the value obtained from Figure 3, G0n= 42.6 KPa, we obtain a value of Me = 49.7 kg/mol. The slope below the critical M is ∼1.2±0.02 and Mc ≈ 105. The former indicates Rouse-like (unentangled) behavior, and the value is remarkably similar to recent reports on bottlebrush polymers with atactic polypropylene (a-PP) side chains (slope ≈ 1.2).23,24 A slope of 1.2 was associated with extended cylindrical chain conformations arising from the high branching density. (The a-PP branches are relatively short and unentangled.) However, unlike the a-PP bottlebrush polymers,22 the PF polymers display a distinct transition to entangled chain dynamics, but at a rather high Mc compared with flexible linear polymers (i.e., Mc (PF) ≈ 105 g/mol versus Mc (cis-1,4 PI)25 ≈ 104 g/mol). Because the PF pendant groups are relatively short (C11 and C13) and well below the entanglement M for linear PI, the implication is that highmolecular-weight PF behaves like an entangled polymer melt with a large molecular weight between backbone entangle-
Figure 8. Molecular weight dependence of the PF dielectric spectra at different temperatures as indicated. The dielectric loss is rescaled by its α-peak height and presented as a function of the reduced frequency. D
DOI: 10.1021/acs.macromol.8b00851 Macromolecules XXXX, XXX, XXX−XXX
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respectively29), we assign this process to global end-to-end chain relaxation (the dielectric normal mode). VFT dependence is observed for the normal mode, in keeping with the cooperative nature of this process.22,30 To put our findings on the polyfarnesenes into context, we first consider the crossed gray symbols in Figure 5: These data are from the literature for the dielectric normal mode for linear PI under isofriction conditions (τn/τα).19−22 For oligomeric melts of flexible chains below a critical molecular weight, the dependence of the normal mode relaxation is predicted to scale as τn ∝ Mz, with z = 2 indicative of Rouse dynamics.19 This is has been confirmed by the experimental results in a number of other studies of the dielectric normal mode of linear oligomeric PI.23,25,26,31−33 The collected τn data in Figure 5 for PI at M > Mc yield an exponent of ∼3.5.29,31,34 The dependence of τn on Mw is displayed for the nine PFs in Figure 5, on the main plot and in the inset. The data on the main plot are the “raw” τn values, and those in the inset are for isofriction conditions (that is, τn relative to τα). However, informed by the rheology data and experimental Mc, it is not unreasonable to suggest a molecular weight dependence of log τn/τα with slope ∼2.0 at M < Mc and a steeper slope of ∼3.4 above a critical M ≈ 105 g/mol. Considering the log τn data in this fashion, like the rheology data, Rouse-like dynamics are indicated for Mw < Mc.
Figure 9. Mean relaxation rates for the glassy state β relaxation, ωβ, the segmental process, ωα, and the normal mode relaxation (ωn) for PFs with different Mw versus inverse temperature. The solid lines are fits using the VFT and Arrhenius equations. The dashed line labeled TgBDS indicates the extrapolation of the VFT fits to 100 s. The TgBDS values are identical to those from DSC and LVE within experimental uncertainty (Table S1).
Figure 8 shows the Mw dependence of the dielectric spectra in a plot of reduced permittivity versus reduced frequency in the region of the normal mode and α processes. As expected, as Mw increases the normal mode process shifts to lower reduced frequencies. By plotting the ratio of the relaxation time of the normal mode to that of the α relaxation process, one can obtain the Mw dependence of the normal mode under isofrictional conditions, and the findings are compared later with well-known PI under the same conditions. The low-temperature processes (β) coincide for all PF samples within the limits of experimental accuracy. Typical of glassy state processes, the β relaxation follows an Arrhenius temperature dependence [ωβ(T) = ω0 exp(−Ea/RT)] with mean activation energy (Ea) = 28 kJ/mol. The precise origin of the PF glassy state process is unknown at present, although we speculate that the origin of this relaxation is associated with PF side group motions in the glassy state rather than a Johari− Goldstein relaxation (with Ea ≈ 38 kJ/mol), as proposed for high-cis-content 1,4-PI and 1,4-polybutadiene.27,28 The α relaxations (dynamic Tg values) are observed at somewhat higher temperatures, and the relaxation frequencies (ωα) follow Vogel−Fulcher−Tammann (VFT) temperature dependence, typical for cooperative processes (Figure 9):
( ),
ωα(T ) = ω∞ exp
B T − T0
4. CONCLUSIONS Polyfarnesenes exhibit log η0 − log Mw scaling exponents of ∼1.2 and ∼3.1 below and above a critical Mw ≈105 g/mol, respectively. That is, Rouse-like dynamics are observed below Mc, and, given the densely packed C11/C13 pendants, we interpret this as arising from their bottlebrush-like nature. At higher Mw, however, PF behaves as an entangled polymer melt, with rather large molecular weight between backbone entanglements (∼50 000 g/mol). Dielectric spectroscopy measurements establish that PF is a type-A polymer, exhibiting a distinct normal mode relaxation whose relaxation time is strongly dependent on Mw. Considering the relatively modest number of PFs explored in this investigation, the M w dependence of log τn is in keeping the molecular picture derived from the oscillatory shear experiments.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00851. Figure S.1: Dynamic master curves of storage and loss moduli for all PF samples from the terminal region to the glassy state at a reference temperature of Tref = 293 K. Frequency shift factors (aT) used to generate the master curves as a function of T − Tg. Table S1. VFT fitting parameters for the dielectric α relaxations and Tg BDS. Table S2. Weight-average molecular weights and densities for PF under study. (PDF)
where ω∞, B, and T0 (Vogel
temperature) are temperature-independent fitting parameters.16 Parameters for the VFT fits are provided in Table S1. As seen in Figure 9, ωα are very similar for PFs spanning nearly two orders of magnitude of molecular weight. VFT fits of ωα versus 1000/T were extrapolated to 100 s to estimate Tg values from dielectric spectroscopy. The extrapolated values (Table S1) correspond very well with those determined from DSC and LVE (Table 1), with all findings indicating a slight increase in Tg with molecular weight. Unlike the α and β processes, the highest temperature dielectric process is very strongly dependent on PF molecular weight (Figure 9). Considering the net parallel dipole moment contribution along the PF chain backbone (parallel dipoles moments have been estimated using ab initio calculations to be 0.132 and 0.045 D for cis- and trans-1,4 structures,
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AUTHOR INFORMATION
Corresponding Authors
*J.R.: E-mail:
[email protected]. *C.I.: E-mail:
[email protected]. ORCID
Ciprian Iacob: 0000-0001-7982-0586 E
DOI: 10.1021/acs.macromol.8b00851 Macromolecules XXXX, XXX, XXX−XXX
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(19) Imanishi, Y.; Adachi, K.; Kotaka, T. Further Investigation of the Dielectric Normal Mode Process in Undiluted Cis-Polyisoprene with Narrow Distribution of Molecular Weight. J. Chem. Phys. 1988, 89, 7585−7592. (20) Adachi, K.; Yoshida, H.; Fukui, F.; Kotaka, T. Comparison of Dielectric and Viscoelastic Relaxation Spectra of Polyisoprene. Macromolecules 1990, 23, 3138−3144. (21) Matsumiya, Y.; Watanabe, H.; Osaki, K. Comparison of Dielectric and Viscoelastic Relaxation Functions of cis-Polyisoprenes: Test of Tube Dilation Molecular Picture. Macromolecules 2000, 33, 499−506. (22) Sato, T.; Watanabe, H.; Osaki, K.; Yao, M.-L. Relaxation of Spherical Micellar Systems of Styrene-Isoprene Diblock Copolymers. 1. Linear Viscoelastic and Dielectric Behavior. Macromolecules 1996, 29, 3881−3889. (23) Dalsin, S. J.; Hillmyer, M. A.; Bates, F. S. Molecular Weight Dependence of Zero-Shear Viscosity in Atactic Polypropylene Bottlebrush Polymers. ACS Macro Lett. 2014, 3, 423−427. (24) Dalsin, S. J.; Hillmyer, M. A.; Bates, F. S. Linear Rheology of Polyolefin-Based Bottlebrush Polymers. Macromolecules 2015, 48, 4680−4691. (25) Abdel-Goad, M.; Pyckhout-Hintzen, W.; Kahle, S.; Allgaier, J.; Richter, D.; Fetters, L. J. Rheological Properties of 1,4-Polyisoprene over a Large Molecular Weight Range. Macromolecules 2004, 37, 8135−8144. (26) Fetters, L. J.; Lohse, D. J.; Richter, D.; Witten, T. A.; Zirkel, A. Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties. Macromolecules 1994, 27, 4639−4647. (27) Roland, C. M.; Schroeder, M. J.; Fontanella, J. J.; Ngai, K. L. Evolution of the Dynamics in 1,4-Polyisoprene from a Nearly Constant Loss to a Johari-Goldstein β-Relaxation to the α-Relaxation. Macromolecules 2004, 37, 2630−2635. (28) Kudlik, A.; Benkhof, S.; Blochowicz, T.; Tschirwitz, C.; Rössler, E. The Dielectric Response of Simple Organic Glass Formers. J. Mol. Struct. 1999, 479, 201−218. (29) Cerveny, S.; Zinck, P.; Terrier, M.; Arrese-Igor, S.; Alegría, A.; Colmenero, J. Dynamics of Amorphous and Semicrystalline 1,4-transPoly(isoprene) by Dielectric Spectroscopy. Macromolecules 2008, 41, 8669−8676. (30) Mijovic, J.; Sun, M.; Han, Y. Normal and Segmental Mode Dynamics of End-Functionalized Poly(propylene oxide) by Dielectric Relaxation Spectroscopy and Dynamic Mechanical Spectroscopy. Macromolecules 2002, 35, 6417−6425. (31) Watanabe, H. Dielectric Relaxation of Type-A Polymers in Melts and Solutions, Macromol. Macromol. Rapid Commun. 2001, 22, 127−175. (32) Riedel, C.; Alegria, A.; Tordjeman, P.; Colmenero, J. RouseModel-Based Description of the Dielectric Relaxation of Nonentangled Linear 1,4-cis-Polyisoprene. Macromolecules 2009, 42, 8492−8499. (33) Boese, D.; Kremer, F. Molecular Dynamics in Bulk cisPolyisoprene As Studied by Dielectric Spectroscopy. Macromolecules 1990, 23, 829−835. (34) Abou Elfadl, A.; Kahlau, R.; Herrmann, A.; Novikov, V. N.; Rössler, E. A. From Rouse to Fully Established Entanglement Dynamics: A Study of Polyisoprene by Dielectric Spectroscopy,. Macromolecules 2010, 43, 3340−3351.
James Runt: 0000-0002-8630-1239 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation, Division of Materials Research, Polymers Program through DMR-1505953. We thank Steven Henning (Total Cray Valley) for many fruitful discussions. We also thank Jacob Lanasa and Renxuan Xie (Penn State University) for SEC measurements and support with rheological measurements, respectively.
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REFERENCES
(1) Farnesene | The Renewable Hydrocarbon Building Block. https:// farnesene.net/. (2) Yoo, T.; Henning, S. K. The Synthesis and Characterization of Farnesene-based Polymers. Rubber Chem. Technol. 2017, 90, 308. (3) Vlassopoulos, D.; Fytas, G.; Loppinet, B.; Isel, F.; Lutz, P.; Benoit, H. Polymacromonomers: Structure and Dynamics in Nondilute Solutions, Melts, and Mixtures. Macromolecules 2000, 33, 5960−5969. (4) Inoue, T.; Matsuno, K.; Watanabe, H.; Nakamura, Y. Rheooptical Study on Poly(styrene macromonomer). Macromolecules 2006, 39, 7601−7606. (5) Berry, G. C.; Kahle, S.; Ohno, S.; Matyjaszewski, K.; Pakula, T. Viscoelastic and Dielectric Studies on Comb- and Brush-shaped Poly(n-butyl acrylate). Polymer 2008, 49, 3533−3540. (6) Hu, M.; Xia, Y.; McKenna, G. B.; Kornfield, J. A.; Grubbs, R. H. Linear Rheological Response of a Series of Densely Branched Brush Polymers. Macromolecules 2011, 44, 6935−6943. (7) Iwawaki, H.; Urakawa, O.; Inoue, T.; Nakamura, Y. RheoOptical Study on Dynamics of Bottlebrush-Like Polymacromonomer Consisting of Polystyrene. II. Side Chain Length Dependence on Dynamical Stiffness of Main Chain. Macromolecules 2012, 45, 4801− 4808. (8) Adachi, K.; Kotaka, T. Dielectric Normal Mode Relaxation. Prog. Polym. Sci. 1993, 18, 585−622. (9) Schönhals, A. Relation between Main and Normal Mode Relaxations for Polyisoprene Studied by Dielectric Spectroscopy. Macromolecules 1993, 26, 1309−1312. (10) Fukao, K. Dynamics in Thin Polymer Films by Dielectric Spectroscopy. Eur. Phys. J. E: Soft Matter Biol. Phys. 2003, 12, 119− 125. (11) Casalini, R.; Roland, C. M. Temperature and Density Effects on the Local Segmental and Global Chain Dynamics of Poly(oxybutylene). Macromolecules 2005, 38, 1779−1788. (12) Gerstl, C.; Schneider, G. J.; Pyckhout-Hintzen, W.; Allgaier, J.; Richter, D.; Alegría, A.; Colmenero, J. Segmental and Normal Mode Relaxation of Poly(alkylene oxide)s Studied by Dielectric Spectroscopy and Rheology. Macromolecules 2010, 43, 4968−4977. (13) Gainaru, C.; Hiller, W.; Böhmer, R. A. Dielectric Study of Oligo- and Poly(propylene glycol). Macromolecules 2010, 43, 1907− 1914. (14) Mori, S., Barth, G. H. Size Exclusion Chromatography (Springer Laboratory); Springer-Verlag, 1999. (15) Xie, R.; Lee, Y.; Aplan, M. P.; Caggiano, N. J.; Müller, C.; Colby, R. H.; Gomez, E. D. Glass Transition Temperature of Conjugated Polymers by Oscillatory Shear Rheometry. Macromolecules 2017, 50, 5146−5154. (16) Broadband Dielectric Spectroscopy; Kremer, F., Schönhals, A., Eds.; Springer-Verlag: Heidelberg, Germany, 2002. (17) Rubenstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: Oxford, U.K., 2003. (18) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, U.K., 1988. F
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