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

Wischnewski, A.; Monkenbusch, M.; Willner, Lutz; Richter, D.; Likhtman, Alexei E.; McLeish, Tom; Faragó, B.

doi:10.1103/physrevlett.88.058301

Cited by 102 publications

(127 citation statements)

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“…Applying the proper corrections for nonGaussianity effects the self-motion of a segment quantitatively agrees with the expectation of a tube model with parameters as obtained from the coherent single chain structure factor [9].…”

Section: P H Y S I C a L R E V I E W L E T T E R S Week Endingsupporting

confidence: 59%

“…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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confidence: 91%

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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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Section: P H Y S I C a L R E V I E W L E T T E R S Week Endingsupporting

confidence: 59%

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confidence: 91%

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

et al. 2003

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“…This relaxation is attributed to contour length fluctuations. 14 Now we shall try to describe the standard tube model and compare it to the data in Figure 1. The tube model assumes that, at early t < τ e , the motion of the chain obeys Rouse dynamics, in accordance with experiment.…”

Section: Current "Standard" Tube Model and Nsementioning

confidence: 99%

“…It is the only polymer that is extensively studied by NSE for times well over τ e and for a variety of molecular weights (see ref 14 and references therein). Thus, I will fit the model to NSE experiments first and then predict rheology and diffusion.…”

Section: Polyethylene (Pe)mentioning

confidence: 99%

Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

2005

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The model presented in this paper describes simultaneously three different experimental techniques applied to different monodisperse polymer melts: neutron spin-echo (NSE), linear rheology, and diffusion. First, it shows that the standard tube model cannot be applied to NSE because the statistics of a one-dimensional (1D) chain in a three-dimensional (3D) random-walk tube become wrong on the length scale of the tube diameter, whereas all available NSE data are for scattering vectors in this range. Then a new single-chain dynamic slip-link model on the basis of a recent network model by Rubinstein and Panyukov is introduced. Instead of solving the model analytically, which would require uncontrolled approximations, the model is formulated in terms of stochastic differential equations, suitable for Brownian dynamics simulations. I perform these simple simulations, demonstrate that the model describes individual experiments well, and then compare the results with experiments on monodisperse polyethylene, polyethylene-propylene, polyisoprene, polybutadiene, and polystyrene. For all polymers, model parameters from one experiment are obtained, and the others are predicted without fitting. The results show some systematic discrepancies, suggesting possible inadequacy of the Gaussian chain model for some of the polymers, and possible inadequacy of time-temperature superposition.

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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%

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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Briels

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

Cited by 102 publications

References 10 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

Single-Chain Slip-Link Model of Entangled Polymers: Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

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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