Clear Evidence of Reptation in Polyethylene from Neutron Spin-Echo Spectroscopy

Schleger, P.; Faragó, B.; Lartigue, C.; Kollmar, A.; Richter, D.

doi:10.1103/physrevlett.81.124

Cited by 138 publications

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“…Also a transition to a regime with a different power law compatible with / t 1=4 is clearly visible. However, the crossover occurs at about e ' 1 ns which is much less than the textbook value [8] derived as e DE d 4 = 36Wl 4 ' 7 ns, where the elementary step length of the Gaussion contorted virtual tube is identified with the tube diameter (d 4:8 nm [7,9]). Following Refs.…”

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Direct Observation of the Transition from Free to Constrained Single-Segment Motion in Entangled Polymer Melts

et al. 2003

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We report a direct determination of the time dependent mean-squared segment displacement of a polymer chain in the melt covering the transition from free to constraint Rouse relaxation along the virtual tube of the reptation model. This has been achieved by a neutron spin-echo (NSE) measurement of the segmental self-correlation function as conveyed by the spin-incoherent scattering from two fully protonated polymer melts, polyethylene and polyethylene propylene. Within the scenario of de Gennes reptation model a transition of the time dependence of segmental mean-squared displacements from / t 1=2 to / t 1=4 is expected and clearly corroborated by the incoherent NSE results. DOI: 10.1103/PhysRevLett.90.058302 PACS numbers: 47.50.+d, 83.10.Kn Beyond a certain length polymer chains in a melt are subject to topological constraints of motion due to entanglements. As a consequence in high molecular weight (M) melts the viscosity becomes proportional to M 3:4 instead of / M for low molecular weights [1]. Furthermore in the viscoelastic properties of the melt at intermediate frequency ! a plateau in the modulus G ! , i.e., a transient rubbery network is observed [2]. A comprehensive recent review on viscoelasticity in entangled polymers may be found in Ref. [3]. Microscopically the single chain structure factor S Q; t as observed by neutron spin-echo (NSE) spectroscopy on deuterated melts containing a few h-labeled chains provides clear evidence for the restriction of motion [4,5] and corrobates all the features of the de Gennes dynamic structure factor for local reptation [6 -9]. The mean-squared segmental displacements hr 2 t i in the reptation scenario are given by an initial entropy driven Rouse motion [hr 2 t i / t 1=2 ] for t < e . At e the segmental diffusion slows down due to the ''contact'' with the ''walls'' of the virtual tube, further motion, termed local reptation, is a quasi-onedimensional Rouse relaxation along the contour of the virtual tube [hr 2 t i / t 1=4 ] [8]. This work presents the first direct measurements of hr 2 t i in space and time in terms of the proton self-correlation function of diffusing segments in long chain polyethylene (PE) and polyethylene propylene (PEP) melts. The measured self-correlation function very clearly displays the predicted crossover from free Rouse motion to local reptation. Considering the non-Gaussian character of the segment motion along a 1D contorted tube, in the frame of the reptation model the single chain dynamic structure factor and the selfcorrelation function agree quantitatively. The resulting tube diameter thereby is significantly larger than what is inferred from rheology [10,11].The PE and PEP samples were obtained from parent 1,4-polybutadiene and polyisoprene, respectively, which were synthesized by anionic polymerization [12]. PE and PEP were obtained by subsequent hydrogenation (deuteration). For the present investigations PE with a molecular weight M w 190 kg=mol and PEP with M w 80 kg=mol was chosen, both well in the entangled state.The incoher...

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Direct Observation of the Transition from Free to Constrained Single-Segment Motion in Entangled Polymer Melts

et al. 2003

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“…Richter and co-workers 6,14,15 have performed NSE experiments on high molecular weight PE melts. For the single-chain coherent dynamic structure factor, they found very good agreement with the predictions of the reptation model.…”

Section: A Coherent Dynamic Structure Factormentioning

confidence: 99%

“…Time-resolved experiments measure the dynamics of the system with sufficiently small time resolution to be able to probe a relevant time dependent correlation function before it reaches its long time limit. Examples are neutron spin-echo ͑NSE͒ spectroscopy, 6 measuring the coherent dynamic structure factor, proton and deuteron field-cycling NMR relaxometry, 7 probing the Kuhn segment tangent vector correlation function, and NMR field-gradient diffusometry ͑when applied to relatively short time-scales͒, 8 probing the mean-squared displacement of Kuhn segments. On the other hand, time-integrated experiments either integrate over a long-time or measure the long-time limit of some correlation function, which amounts to integrating its time derivative.…”

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A time-integrated estimate of the entanglement mass in polymer melts in agreement with the one determined by time-resolved measurements

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2004

The Journal of Chemical Physics

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Effects of alignment layer thickness on the pretilt angle of liquid crystals APL: Org. Electron. Photonics 3, 270 (2010) Effects of alignment layer thickness on the pretilt angle of liquid crystals Appl. Phys. Lett. 97, 243306 (2010) Field-theoretic model of inhomogeneous supramolecular polymer networks and gels J. Chem. Phys. 133, 174903 (2010) Origin of translocation barriers for polyelectrolyte chains JCP: BioChem. Phys We make a critical examination of how the entanglement molecular mass M e is determined from various measurable quantities. We are guided by reptation theory, where it is assumed that characteristic relaxations abruptly change and become equal to those of a chain moving in a Gaussian tube, as soon as the corresponding length scales surpass the tube diameter d or similarly as soon as the corresponding mass surpasses a critical value. Taking this critical mass as a definition of the ''reptational'' entanglement mass, we observe that all methods based on time-resolved quantities, such as the single-chain dynamic structure factor S(q,t) and the zero-shear relaxation modulus G(t), give the same result. We observe that such a value differs, beyond error bars, from that obtained from the plateau modulus, which is a time-integrated quantity. We have investigated an alternative definition of entanglement mass in terms of time-integrated quantities and observe that the value of this specific entanglement mass is consistent with that obtained from the time-resolved observables. We comment on possible reasons for the plateau modulus discrepancy.

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“…Schleger et al showed that the dynamic-structure factor of the reptation model was corroborated, while all other competing models, which predict structure factors, performed far less well [6].…”

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“…Although the reptation model treated at this level is able to describe macroscopic melt dynamics qualitatively, as expressed by measurements of rheology and diffusion, it was shown by Doi a long time ago [3] that, in order to achieve even semiquantitative agreement with the rheology of polymer melts at time scales less than Rouse time, one needs an additional mechanism of chain motion, namely, contour-length fluctuations. Rheology is an indirect probe of molecular motion, but very recently it became possible to observe the tube confinement and the associated restrictions of segment motion directly in space and time [4][5][6].…”

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Molecular Observation of Contour-Length Fluctuations Limiting Topological Confinement in Polymer Melts

et al. 2002

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Clear Evidence of Reptation in Polyethylene from Neutron Spin-Echo Spectroscopy

Cited by 138 publications

References 19 publications

Direct Observation of the Transition from Free to Constrained Single-Segment Motion in Entangled Polymer Melts

Direct Observation of the Transition from Free to Constrained Single-Segment Motion in Entangled Polymer Melts

A time-integrated estimate of the entanglement mass in polymer melts in agreement with the one determined by time-resolved measurements

Molecular Observation of Contour-Length Fluctuations Limiting Topological Confinement in Polymer Melts

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