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Zhu ZY, Gou WW, Chen JH, Zhang QG, Zhu AM, Liu QL. Crosslinked naphthalene-based triblock polymer anion exchange membranes for fuel cells. J Memb Sci 2021. [DOI: 10.1016/j.memsci.2021.119569] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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2
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Ostrovskaya IK, Fatkullin NF, Körber T, Rössler EA, Lozovoi A, Mattea C, Stapf S. On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics. J Chem Phys 2020; 152:184904. [PMID: 32414263 DOI: 10.1063/5.0005049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times. With an increase in observation time, the contribution from end effects to the FID increases. In the regime of incoherent reptation, contributions to the FID from central segments yield an exponent of 1/4 for the stretched decay and contributions from end segments yield an exponent of 3/16. In the regime of coherent reptation, the central segments generate a stretching exponent of 1/2, whereas the end segments contribute with an exponent of 1/4. These predictions are shown to be in qualitative agreement with the experimental FIDs of perdeuterated poly(ethylene oxide) with molecular masses of 132 kg/mol and 862 kg/mol.
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Affiliation(s)
- I K Ostrovskaya
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - N F Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - T Körber
- Inorganic Chemistry III and Northern Bavarian NMR Centre, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - E A Rössler
- Inorganic Chemistry III and Northern Bavarian NMR Centre, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - A Lozovoi
- Department of Physics, CUNY-The City College of New York, New York, New York 10031, USA
| | - C Mattea
- Department of Technical Physics II/Polymer Physics, TU Ilmenau, P.O. Box 100 565, D-98684 Ilmenau, Germany
| | - S Stapf
- Department of Technical Physics II/Polymer Physics, TU Ilmenau, P.O. Box 100 565, D-98684 Ilmenau, Germany
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Golmohammadi N, Boland-Hemmat M, Barahmand S, Eslami H. Coarse-grained molecular dynamics simulations of poly(ethylene terephthalate). J Chem Phys 2020; 152:114901. [PMID: 32199431 DOI: 10.1063/1.5145142] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
We have constructed efficient coarse-grained (CG) models of poly(ethylene terephthalate) (PET), using three mapping schemes, in which a repeat unit is lumped into either three or four beads. The CG potentials are parameterized to reproduce target distributions of an underlying accurate atomistic model [H. Eslami and F. Müller-Plathe, Macromolecules 42, 8241-8250 (2009)]. The CG simulations allow equilibration of long PET chains at all length scales. The CG results on the density of PET in melt and glassy states, chain dimension, local packing, and structure factor are in good agreement with experiment. We have established a link between the glass transition temperature and the local movements including conformational transitions and mean-square displacements of chain segments. Temperature transferabilities of the three proposed models were studied by comparing CG results on the static and thermodynamic properties of a polymer with atomistic and experimental findings. One of the three CG models has a good degree of transferability, following all inter- and intra-structural rearrangements of the atomistic model, over a broad range of temperature. Furthermore, as a distinct point of strength of CG, over atomistic, simulations, we have examined the dynamics of PET long chains, consisting of 100 repeat units, over a regime where entanglements dominate the dynamics. Performing long-time (550 ns) CG simulations, we have noticed the signature of a crossover from Rouse to reptation dynamics. However, a clear separation between the Rouse and the reptation dynamics needs much longer time simulations, confirming the experimental findings that the crossover to full reptation dynamics is very protracted.
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Affiliation(s)
- Nazila Golmohammadi
- Department of Chemistry, College of Sciences, Persian Gulf University, Boushehr 75168, Iran
| | | | - Sanam Barahmand
- Department of Chemistry, College of Sciences, Persian Gulf University, Boushehr 75168, Iran
| | - Hossein Eslami
- Department of Chemistry, College of Sciences, Persian Gulf University, Boushehr 75168, Iran
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4
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Lozovoi A, Mattea C, Fatkullin N, Stapf S. Segmental Dynamics of Entangled Poly(ethylene oxide) Melts: Deviations from the Tube-Reptation Model. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Lozovoi
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - C. Mattea
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, 420008 Kazan, Tatarstan, Russia
| | - S. Stapf
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
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5
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Affiliation(s)
- Marius Hofmann
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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6
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Mohamed F, Flämig M, Hofmann M, Heymann L, Willner L, Fatkullin N, Aksel N, Rössler EA. Scaling analysis of the viscoelastic response of linear polymers. J Chem Phys 2018; 149:044902. [PMID: 30068172 DOI: 10.1063/1.5038643] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Viscoelastic response in terms of the complex shear modulus G*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature Tg (174 K-373 K). Master curves G'(ωτα) and G″(ωτα) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to Tg is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τα used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτα) ∝ ωε″. The exponent ε″ = ε″(ωτα) ≡ d ln G″(ωτα)/d ln(ωτα) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτα). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = -0.25), i.e., G″(ω) ∝ ω-0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτα) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τe. However, as the exponent in the Rouse regime (ωτe > 1) varies along εeRouse = 0.66 ± 0.04 (off the Rouse prediction εRouse = 0.5) and that at ωτe < 1 is similar, only a weak manifestation of the crossover at τe is found at highest M. Yet, calculating τe/τα= (M/Mo)2, we find good agreement among the polymers when discussing ε″(ωτe). The terminal relaxation time τt is directly read off from ε″(ωτα). Plotting τt/τe as a function of Z = M/Me, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτα) scales as τmin ∝ M1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.
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Affiliation(s)
- F Mohamed
- Experimentalphysik II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - M Flämig
- Experimentalphysik II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - M Hofmann
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - L Heymann
- Technische Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - L Willner
- Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - N Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - N Aksel
- Technische Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - E A Rössler
- Experimentalphysik II, Universität Bayreuth, D-95440 Bayreuth, Germany
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7
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Fatkullin N, Körber T, Rössler E. Signature of reptation in the long-time behavior of the deuteron NMR Free Induction Decay in high molecular mass polymer melts. POLYMER 2018. [DOI: 10.1016/j.polymer.2018.03.050] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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8
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Lozovoi A, Petrova L, Mattea C, Stapf S, Rössler EA, Fatkullin N. On the theory of the proton dipolar-correlation effect as a method for investigation of segmental displacement in polymer melts. J Chem Phys 2017; 147:074904. [DOI: 10.1063/1.4998184] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- A. Lozovoi
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - L. Petrova
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - C. Mattea
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - S. Stapf
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - E. A. Rössler
- Department Experimentalphysik II, University of Bayreuth, 95440 Bayreuth, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
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9
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Kimmich R, Fatkullin N. Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2017; 101:18-50. [PMID: 28844220 DOI: 10.1016/j.pnmrs.2017.04.001] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Revised: 04/02/2017] [Accepted: 04/02/2017] [Indexed: 06/07/2023]
Abstract
Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under entanglement and chain connectivity constraints. Under such conditions, reorientations will be correlated with translational displacements leading to the so-called RMTD relaxation process (reorientation mediated by translational displacements). Applications to porous glasses, protein solutions, lipid bilayers, and clays will be discussed. Finally, we will address the intriguing fact that the various time limits of the segment mean-square displacement of polymers in some cases perfectly reproduce predictions of the tube/reptation model whereas the reorientation dynamics suggests strongly deviating power laws.
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Affiliation(s)
| | - Nail Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008 Tatarstan, Russia
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10
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Lozovoi A, Mattea C, Hofmann M, Saalwaechter K, Fatkullin N, Stapf S. Segmental dynamics of polyethylene-alt-propylene studied by NMR spin echo techniques. J Chem Phys 2017; 146:224901. [PMID: 29166039 DOI: 10.1063/1.4984265] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Segmental dynamics of a highly entangled melt of linear polyethylene-alt-propylene with a molecular weight of 200 kDa was studied with a novel proton nuclear magnetic resonance (NMR) approach based upon 1H → 2H isotope dilution as applied to a solid-echo build-up function ISE(t), which is constructed from the NMR spin echo signals arising from the Hahn echo (HE) and two variations of the solid-echo pulse sequence. The isotope dilution enables the separation of inter- and intramolecular contributions to this function and allows one to extract the segmental mean-squared displacements in the millisecond time range, which is hardly accessible by other experimental methods. The proposed technique in combination with time-temperature superposition yields information about segmental translation in polyethylene-alt-propylene over 6 decades in time from 10-6 s up to 1 s. The time dependence of the mean-squared displacement obtained in this time range clearly shows three regimes of power law with exponents, which are in good agreement with the tube-reptation model predictions for the Rouse model, incoherent reptation and coherent reptation regimes. The results at short times coincide with the fast-field cycling relaxometry and neutron spin echo data, yet, significantly extending the probed time range. Furthermore, the obtained data are verified as well by the use of the dipolar-correlation effect on the Hahn echo, which was developed before by the co-authors. At the same time, the amplitude ratio of the intermolecular part of the proton dynamic dipole-dipole correlation function over the intramolecular part obtained from the experimental data is not in agreement with the predictions of the tube-reptation model for the regimes of incoherent and coherent reptation.
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Affiliation(s)
- A Lozovoi
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - C Mattea
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - M Hofmann
- Department of Chemistry, Louisiana State University, 70803 Baton Rouge, Louisiana, USA
| | - K Saalwaechter
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle (Saale), Germany
| | - N Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - S Stapf
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
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11
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Kresse B, Becher M, Privalov AF, Hofmann M, Rössler EA, Vogel M, Fujara F. 1H NMR at Larmor frequencies down to 3Hz by means of Field-Cycling techniques. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 277:79-85. [PMID: 28258024 DOI: 10.1016/j.jmr.2017.02.002] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 01/30/2017] [Accepted: 02/02/2017] [Indexed: 06/06/2023]
Abstract
Field-Cycling (FC) NMR experiments were carried out at 1H Larmor frequencies down to about 3Hz. This could be achieved by fast switching a high polarizing magnetic field down to a low evolution field which is tilted with respect to the polarization field. Then, the low frequency Larmor precession of the nuclear spin magnetization about this evolution field is registered by means of FIDs in a high detection field. The crucial technical point of the experiment is the stabilization of the evolution field, which is achieved by compensating for temporal magnetic field fluctuations of all three spatial components. The paper reports on some other basic low field experiments such as the simultaneous measurement of the Larmor frequency and the spin-lattice relaxation time in such small fields as well as the irradiation of oscillating transversal magnetic field pulses at very low frequencies as a novel method for field calibration in low field FC NMR. The potential of low field FC is exemplified by the 1H relaxation dispersion of water at frequencies below about 2kHz stemming from the slow proton exchange process.
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Affiliation(s)
- B Kresse
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany.
| | - M Becher
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - A F Privalov
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - M Hofmann
- Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA
| | - E A Rössler
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
| | - M Vogel
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
| | - F Fujara
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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12
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Spiess HW. 50th Anniversary Perspective: The Importance of NMR Spectroscopy to Macromolecular Science. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02736] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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13
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Hofmann M, Fatkullin N, Rössler EA. Inconsistencies in Determining the Entanglement Time of Poly(butadiene) from Rheology and Comparison to Results from Field-Cycling NMR. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02546] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. Hofmann
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - N. Fatkullin
- Institute
of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - E. A. Rössler
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
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14
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Hofmann M, Kresse B, Heymann L, Privalov AF, Willner L, Fatkullin N, Aksel N, Fujara F, Rössler EA. Dynamics of a Paradigmatic Linear Polymer: A Proton Field-Cycling NMR Relaxometry Study on Poly(ethylene–propylene). Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01906] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Hofmann
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - B. Kresse
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - L. Heymann
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - A. F. Privalov
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - L. Willner
- Institute
of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - N. Fatkullin
- Institute
of Physics, Kazan Federal University, Kazan 420008, Tatarstan Russia
| | - N. Aksel
- Technische
Mechanik und Strömungsmechanik, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - F. Fujara
- Institut
für Festkörperphysik, TU Darmstadt, D-64289 Darmstadt, Germany
| | - E. A. Rössler
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
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