Time-Domain NMR Observation of Entangled Polymer Dynamics: Focus on All Tube-Model Regimes, Chain Center, and Matrix Effects

Abstract

Proton multiple-quantum time-domain NMR combined with time–temperature superposition is a powerful method to study entangled chain dynamics. Overcoming the previous limitation to regimes II–IV of the tube model, this study extends the method to regime I (localized Rouse motions) by use of a pulse sequence adapted to shorter times, thus covering all relevant regimes for the model case of poly­(butadiene) with molecular weights (M) between 10 and 200 kDa. We determine a value for the entanglement time that is consistent with current rheological results and confirm a value below 1 for the time scaling exponent of the segmental orientation autocorrelation function (OACF) in regime I previously observed by other NMR techniques. The origins of deviations from tube-model predictions are assessed by focusing on the dynamics of the chain centers in end-chain deuterated triblock samples and by dilution of probe chains to 15% in a deuterated matrix with M of 2 MDa. The study is complemented by self-diffusion coefficients measured by pulsed-gradient NMR. Our OACF-based results for the terminal time reinforce the current consensus that below a chain length of 30–50 entanglements matrix effects cannot explain the nonideal M-scaling exponent of 3.4 but are responsible for an M-independent slowdown. The protracted approach of the pure local-reptation scaling in regime II is found to be only somewhat reduced for both chain centers and chains in a long matrix, confirming its generic intrachain origin. These microscopic insights could be compared with results from large-scale computer simulations and provide a gauge for theoretical approaches such as those dealing with constraint release and contour-length fluctuations.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

“…It was also found that τd∼M3.27 which is not in perfect accordance with the tube model predictions. In addition, in that study [59] the self-diffusion coefficients was measured by pulsed-gradient NMR [51,61] and the power law exponent was consistent with earlier studies [49,62]. Moreover, in bidisperse mixtures of 1,4 poly(butadiene), the diffusion coefficient of longer chains decreases by either increasing the chain length of short chains or reducing the weight fraction of short chains in the mixture [62].…”

“…The disentanglement time was evaluated as τd∼M3.3 slightly below τd∼M3.4 as the tube model predicts due to constraint release and contour length fluctuations [57]. The entanglement time that is consistent with rheological results [58] was evaluated by Trutschel et al [59]. A time scaling exponent of 0.8 of the segmental orientation autocorrelation function in the Rouse regime was calculated, smaller than the theoretical unity Rouse prediction but in good agreement with Monte Carlo simulations, where the measured exponent was 0.83 [60].…”

“…Moreover, in bidisperse mixtures of 1,4 poly(butadiene), the diffusion coefficient of longer chains decreases by either increasing the chain length of short chains or reducing the weight fraction of short chains in the mixture [62]. These microscopic insights are compared in this review with results from computer simulations and theoretical approaches [59].…”

Chain dynamics in partially cross‐linked polyethylene by combined rheology and NMR‐based molecular rheology

“…23,24 D res can be measured most quantitatively via time-domain double-quantum (DQ) NMR, and even its distribution has been assessed for studying of the network structure in the rubbers. 25 More general investigations have been performed via extracting the segmental dynamics in terms of the orientation autocorrelation function (OACF) of the second Legendre polynomial C(t) = 5 < P 2 (cosθ[t + τ])P 2 (cosθ(t))>, where θ is the instantaneous segmental orientation with respect to the magnetic field, for the cases of monodisperse polymer melts [26][27][28][29] and transient networks. 30,31 In the former case, a good adherence to predictions of the tube-reptation model could be confirmed, including the expected corrections due to constraint release (CR) and contour length fluctuations (CLF).…”

Spatial inhomogeneity, interfaces and complex vitrification kinetics in a network forming nanocomposite

“…[15][16][17][18] The rigid amorphous fraction and the polymer/matrix interphase have been investigated in the literature employing a variety of different systems and techniques. [21][22][23][24][25][26][27][28][29][30][31] A considerable amount of work has been carried out to study the structure and properties of the PNCs, as well as the interfacial layer employing calorimetry. This method is useful to investigate, for instance, the NP-and the interfacerelated changes of the glass transition temperature (T g ), changes in the molecular mobility and temperature dependence of the heat flow.…”