Algorithm for preliminary evaluation of the correlation time of local dynamics in some polymeric materials (original) (raw)
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Polymer chain dynamics and NMR
Advances in Polymer Science
The universal features of polymer dynamics are specifically represented by laws for (anomalous) segment diffusion and chain relaxation modes. Nuclear magnetic resonance (NMR)-based techniques provide direct access to these phenomena. This in particular refers to NMR relaxation and diffusion studies. Methods suitable for this purpose are described in detail. Three basic classes of polymer dynamics models, namely the Rouse model, the tube/reptation model, and the renormalized Rouse models are outlined and discussed with respect to predictions for NMR measurands. A wealth of experimental NMR data are reviewed and compared with predictions of the model theories. It is shown that characteristic features of all three types of models can be verified in great detail provided that the model premisses are suitably mimicked in the experiments. Rouse dynamics is shown to be relevant for polymer melts with molecular weights below the critical value and for solutions of diminished entanglement effect. Features specific for the renormalized Rouse model reveal themselves in the form of high-and low-mode-number limits of the spin-lattice relaxation dispersion. These results are considered to mirror the analytical structure of the Generalized Langevin Equation. Finally, anomalous-diffusion and relaxation laws characteristic for the tube/reptation model can be perfectly reproduced in experiment if the polymer chains are confined in a nanoporous, solid matrix whereas bulk melts are not in accord with these predictions. The dynamics of chains confined in artificial tubes can be treated analytically assuming a harmonic radial potential for the polymer/wall interaction. These results derived for a real tube closely render the characteristic features of the original Doi/Edwards model predicted for a fictitious tube.
The Journal of Chemical Physics, 2002
The frequency and molecular mass dependences of nuclear magnetic resonance spin-lattice relaxation and the time dependence of the mean-squared segment displacement of Kuhn segment chains confined in static straight and randomly coiled tubes with ''soft'' and ''hard'' walls were studied. ''Soft'' walls were modeled in the form of a cylindrical distribution of a harmonic radial potential. This scenario is analytically solvable in contrast to the situation of ''hard'' ͑reflecting͒ walls corresponding to an infinitely deep square-well radial potential. In the latter case, we have therefore employed Monte Carlo simulations using a modified Stockmayer chain model. In both situations, qualitatively equivalent results were obtained. Depending on the effective tube diameter ͑or width of the potential well͒ a crossover from Rouse to reptation behavior occurs which sets on already far beyond the Flory radius of the polymer. In terms of the spin-lattice relaxation dispersion, reptation reveals itself by T 1 ϰM 0 3/4 in the chain mode regime, in good agreement with experimental data for polymers in artificial tubes reported in our previous paper by Kimmich et al.
Journal of Chemical Physics, 2010
Proton NMR phenomena such as spin-lattice relaxation, free-induction decays, and solid echoes are analyzed with respect to contributions by intermolecular dipole-dipole interactions in polymer melts. The intermolecular dipole-dipole correlation function is calculated by taking into account the correlation hole effect characteristic for polymer melts. It is shown that the ratio between the intraand intermolecular contributions to NMR measurands depends on the degree of isotropy of chain dynamics anticipated in different models. This, in particular, refers to the tube/reptation model that is intrinsically anisotropic in clear contrast to n-renormalized Rouse models, where no such restriction is implied. Due to anisotropy, the tube/reptation model predicts that the intramolecular contribution to the dipole-dipole correlation function increases with time relative to the intermolecular contribution. Therefore, the intramolecular contribution is expected to dominate NMR measurands by tendency at long times ͑or low frequencies͒. On the other hand, the isotropic nature of the n-renormalized Rouse model suggests that the intermolecular contribution tends to prevail on long-time scales ͑or low frequencies͒. Actually, theoretical estimations and the analysis of experimental spin-lattice relaxation data indicate that the intermolecular contribution to proton NMR measurands is no longer negligible for times longer than 10 −7 s-10 −6 s corresponding to frequencies below the megahertz regime. Interpretations not taking this fact into account need to be reconsidered. The systematic investigation of intermolecular interactions in long-time/low frequency proton NMR promises the revelation of the dynamic features of segment displacements relative to each other in polymer melts.
Solid State Nuclear Magnetic Resonance, 2009
The Mori-Zwanzig projection operator technique was employed to derive the effective Hamiltonian for spin-segment coupling. The fluctuations of this operator are responsible for spin-lattice relaxation in polymer chains. In detail, dipolar interaction of spins is rigorously analyzed by components representing fluctuations of the Kuhn segment end-to-end vectors and local fluctuations on a length scale shorter than the root mean square Kuhn segment length. The former correspond to the usual coarse-grain picture of polymer chain mode theories. It is shown that these non-local chain modes dominate proton spin-lattice relaxation dispersion of flexible polymers at frequencies up to about 10 8 Hz. A corresponding evaluation of experimental data for polybutadiene melts is presented.
Heterogeneous Polymer Dynamics Explored Using Static 1H NMR Spectra
International Journal of Molecular Sciences, 2020
NMR spectroscopy continues to provide important molecular level details of dynamics in different polymer materials, ranging from rubbers to highly crosslinked composites. It has been argued that thermoset polymers containing dynamic and chemical heterogeneities can be fully cured at temperatures well below the final glass transition temperature (Tg). In this paper, we described the use of static solid-state 1H NMR spectroscopy to measure the activation of different chain dynamics as a function of temperature. Near Tg, increasing polymer segmental chain fluctuations lead to dynamic averaging of the local homonuclear proton-proton (1H-1H) dipolar couplings, as reflected in the reduction of the NMR line shape second moment (M2) when motions are faster than the magnitude of the dipolar coupling. In general, for polymer systems, distributions in the dynamic correlation times are commonly expected. To help identify the limitations and pitfalls of M2 analyses, the impact of activation ener...
NMR molecular dynamic study of high crystalline polymers
Polymer Testing, 2000
Analysis of the dynamic behaviour of two highly crystalline polymers, polyethylene (HDPE) and polypropylene (iPP) was carried out by solution and solid state nuclear magnetic resonance (NMR) to obtain the response of the behaviour of both polymers with respect to the molecular chain dynamics, the chain ordination and the molecular packing. The proton spin-lattice relaxation time in the rotating frame (T 1 H ρ) showed that HDPE is more rigid than iPP, because the chain orientation and the molecular packing are different. T 1 H ρ parameter also depends on the molecular chain dynamics, as a result of the different sequence distribution in the domains