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...

The dynamics of binary polymer blends of few labeled long chains in successively shorter matrix chains has been investigated by neutron spin echo (NSE) spectroscopy. For the first time the effect of constraint release on the chain relaxation has been directly observed on a microscopic scale. Decreasing the matrix chain length reduces the topological confinement until unconfined Rouse motion is observed, when the matrix chains are too short to confine the long chain in a tube. Whereas an analytical description of the effect is not yet available, a new simulation based on the slip-link model shows perfect agreement with the NSE data over the full range of matrix molecular weights. DOI: 10.1103/PhysRevLett.96.238302 PACS numbers: 83.80.Sg, 61.12.Ex The dynamics of linear polymer chains in the melt strongly depends on the chain length: For short, unentangled chains (and for any length at short times) the dynamics is determined by a balance of viscous and entropic forces which can be described by the Rouse model [1]. Here the chains interact solely by local friction with a heat bath, representing the neighboring chains. For long chains topological chain-chain interactions in terms of entanglements become important and are dominating the dynamical behavior. In the famous reptation model these constraints are described by a virtual tube which localizes a given chain and limits its motion to a one-dimensional Rouse motion inside the tube (local reptation) and a slow diffusive creep motion out of the tube (reptation) [2]. Neutron spin echo (NSE) spectroscopy is a powerful tool to explore the different dynamic regimes in polymer melts on a microscopic scale in space and time. While NSE experiments support the tube concept of topological confinement in long chain polymer systems [3,4], a close comparison of linear rheology data with predictions of the tube model indicates the existence of additional processes that release the topological confinement [5], such as fluctuating chain ends which escape the tube confinement (contour length fluctuations, CLF) and the relaxation of the tube itself (constraint release, CR). While CLF is an effect of the confined chain itself [6], CR stems from the movement of the chains building the tube, which of course undergo the same dynamical processes as the confined chain (see Fig. 1).In this Letter we present a neutron spin echo study on binary polymer blends in order to investigate the influence of constraint release on the tube confinement by a systematic variation of the matrix molecular weight. This study demonstrates on a molecular level the increasing loss of confinement with the reduction of the host molecular weight and proves the role of CLF in the constraint release process. With a new slip-links model [7] we simulate the dynamics of polymer melts under consideration of CLF and CR and obtain a good description of the NSE data.The different dynamic processes are reflected in the relaxation of the coherent single chain dynamic structure factor Sq; t. This dynamic structure facto...

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Using neutron spin echo (NSE) spectroscopy and a labeling scheme unique to neutron scattering the motion of a labeled branch point of a three-arm polyethylene star has been observed on a molecular level. The measured dynamic structure factor shows a clear transition to a plateau, signifying the stronger confinement of the star center in comparison to a corresponding center labeled linear chain. A shortening of one star arm to about only one entanglement length leads to the same topological confinement as for the symmetric star within the accessible time range of NSE. This reflects a stronger effect of such a small branch than expected and is consistent with rheological measurements on the same system.

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