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

Abstract

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...

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

“…Figure 14 shows rheology data shifted to reference temperature 298 K for the same sample (M w ) 243 K), as was used in ref 15, compared with the model predictions using parameters obtained by NSE (thick lines). One should pay attention only to the high- frequency region, as it was not possible to simulate such large chains (thus the terminal region is not shown).…”

“…We thus used 57 and 116 beads to simulate 12.4 and 24.7 K polyethylene in Figure 7. Figure 11 shows comparison of the model predictions for the incoherent structure factor measured in ref 15 for the same high M w sample as in Figure 7 at the same temperature T ) 509 K. I give this comparison in two representations, one is actual measured data and another represents the mean-square monomer displacement for some models (this is shown not to be strictly valid for the tube model in ref 27). One concludes that the agreement is satisfactory, and in some sense, the incoherent structure factor provides information about entanglements similar to that of the coherent one.…”

“…This is another polymer for which existing NSE data 15 allows fixing of all model parameters, although only high molecular weight is measured. Figure 13 shows the best fit of the data using two parameters: τ 0 (T ) 492 K) ) 0.39 ns, b sim ) 19 Å.…”

Confining Potential when a Biopolymer Filament Reptates

“…This impedes much progress, from processing of plastics to transport in the cell cytoskeleton. Historically, it is modeled [1][2][3] with increasing sophistication as ''reptation'' of linear chains within a ''tube'' along a coarse-grained snakelike ''primitive path'' [4][5][6][7], but too little is known from experiment about the confining potential, a dynamical property that describes transient localization on time scales less than the disentanglement time, owing to the paucity of methods to do so.…”

Incoherent Neutron Spin-Echo Spectroscopy as an Option to Study Long-Range Lipid Diffusion

“…Protonated membranes hydrated with heavy water were used to enhance the incoherent scattering. We note that, despite the experimental challenges, incoherent NSE experiments have recently been reported [17,18] in aqueous solutions and polymers. We, for …”