Anomalous segment diffusion in polymers and NMR relaxation spectroscopy

Abstract

The dynamics of polymer chains in melts, solutions, and networks was studied by the aid of NMR relaxation spectroscopy. Proton data of the spin-lattice relaxation times in the laboratory and rotating frames, T\ and T\" respectively, and of transverse relaxation curves are reported. Frequency, temperature, concentration, molecular weight, and cross-link density dependences have been investigated. Ti was measured in a frequency range of 103 to 3 X 10s Hz predominantly using the field-cycling technique. The study refers to polyisoprene, polyisobutylene, poly(tetrahydrofuran), polystyrene, polyethylene oxide), polyethylene, and poly(dimethylsiloxane). The range of molecular weights was 103-106. The power laws for the time dependence of the mean-square displacement, <r2) « t1/2 and <r2) = t1-'4, predicted by the Doi/Edwards tube model for coil-internal segment diffusion are shown to have their counterparts in the frequency dependence of the spin-lattice relaxation time which is characterized by power laws = 0•5 and T\« 0•25 in corresponding dynamic ranges. The experimental data can be interpreted on the basis of three components of segment fluctuations. The crucial process is the reorientation of segments as a consequence of translational displacements. The orientation correlation function for this mechanism can be derived directly from limits of the time dependence of the mean-square segment displacements provided that the displacements are guided by the chain contour. The experiments show, on the other hand, that the chain dynamics in length scales less than the Doi/Edwards tube diameter is not compatible with the Rouse model, whereas that of melts below the critical molecular weight and solutions is.

Dependence of Order and Dynamics in Polymers and Elastomers under Deformation Revealed by NMR Techniques

“…between kHz and MHz. For linear PDMS, the relationship T 1 (ν) ∝ ν γ with γ ≈ 0.24 was found, and was confirmed for cross--linked PDMS [7]. Figure 1 presents the effect of uniaxial deformation at λ ≈ 2 parallel to B 0 on PDMS rubber at three different temperatures.…”

“…The change of relaxation times on addition of solvent becomes much more pronounced when experiments are performed at low frequencies. The expected behavior for the relaxation dispersion in solutions has been demonstrated for PDMS in [7,20]: a cross-over from a series of power-law relations T 1 ∝ ν γ to a logarithmic dependence T −1 1 (ω) ∝ ln(1/ωτ s ) is seen with increasing dilution. In Fig.…”

“…Three different regions of power laws describing the relaxation dispersion for the chain modes dynamics of polymers can be distinguished [5]. They have been identified and confirmed experimentally for a number of polymers, among them polybutadiene and polydimethylsiloxane [6,7]. The exponents for polyisoprene were found to be somewhat different [8][9][10], but a power-law was still observed.…”

Physical Origin of Anharmonic Dynamics in Proteins: New Insights From Resolution-Dependent Neutron Scattering on Homomeric Polypeptides

“…The first issue can be neglected when using homogeneous systems like HP; the second one is here faced introducing an effective distance d, related to the length scale explored by H atoms in the time scale ¼ h=ÁE accessed by a spectrometer of resolution ÁE via a generalized diffusion-like relation d ¼ . is related to the diffusion coefficient while 0:5 takes into account a possible subdiffusive behavior, often observed in polymeric systems [20]. The model works if experimental MSDs from different spectrometers can be reproduced by MSD model with the same parameters but ÁE.…”

Recent nuclear magnetic resonance experiments on polymer melts: Comments

“…[1][2][3][4][5][6] While several groups have provided interesting NMR data on polymer melts, we focus on the results presented by Kimmich and co-workers. 1,2 These experiments cover a range of five to six orders of magnitude in frequency, corresponding to an equally wide range of relaxation in the time domain.…”