Relaxation parameters for

A similar continuity in the Tj s through the melting temperature was previously reported for linear polyethylene. (17) We have now investigated the temperature dependence of this quantity, for this polymer, in more detail and have also studied a low density (branched) polyethylene. The results for the poly-ethylenes are summarized in Fig. 8. The new data reported here substantiate the conclusion previously reached for linear polyethylene. A similar conclusion can now be reached for the baclc-bone carbons of low density (branched) polyethylene. The melting temperature for this particular sample, under the crystallization conditions studied, is less than 110°C. (33) Thus, the spin-lattice relaxation parameters for the bac)cbone carbons are the same for both the linear and branched polymers over the temperature range studied here. Changes that occur in Tq as the temperature is reduced below 0°C involve other considerations and will be discussed in detail elsewhere. (22)... 

Proton NMR relaxation parameters have also been determined for polyethylene ( ) and polyethylene oxide (39) in the melting region. The apparent contradiction between the proton spin-lattice relaxation parameter for a high molecular weight linear polyethylene sample at its melting point, with the relaxation measurements, has previously been pointed out. (17) This discrepancy is still maintained with the more detailed results reported here for both types of polyethylene. For the proton relaxation a small, but distinct, discontinuity is reported at the melting teirperature. (38)... 

Table V. Spin-Relaxation Parameters for Suberized Cell Walls...

In both the one-dimensional carbon- or proton-detected INEPT polarization transfer experiment and the two-dimensional proton-detected experiment, one needs to optimize the polarization transfer delay with an estimate of the coupling constant. In addition, the refocusing delay. A, must be set separately for an IS and IS2 spin system. For an IS spin system, the optimum delay is A = (l/4)Jis, whereas for an IS2 system the delay should be set to A = (l/8)Jis to get maximum polarization transfer. If one is interested in, for instance, the determination of relaxation parameters for carbons carrying two protons as well as for CH carbons, this requires separate experiments. 

Table 3. Spin-spin relaxation parameters for crosslinked polyether urethanes ...

Figure 8.14 Convergence for the SOR iterative solution scheme with various over-relaxation parameters for the FD compression molding problem.

The principle by which reff is defined may be used to introduce similar effective relaxation parameters for perturbations of any higher symmetry as well. But the dipolar case, as 8M is, seems to be the most natural. 

The reliability of any attempt at determination or characterization of lignin by NMR is dependent on fortuitous similarities in the various spin relaxation parameters. For example, values of T2(H) for lignins tend to be longer than those for cellulose or hemicellulose (Newman 1987, Tekely and Vignon 1987), but the differences are too small to be important for typical values of tp. Values of TI/((H) are sometimes indistinguishable for various components of a sample, and even when differences have been observed, the values are so long that the differences would have little effect on the results (Gerasimowicz et al. 1984, Haw et al. 1984, Maciel et al. 1985). 

Table 3 Relaxation parameters for molecular motion in crystalline (T) -C5Me5)2Fe2(p-00)2(00)2, (Ti -C5Me5)2Cr2(CO)4, (Ti -C5Me5)Rh(CO)2 and comparison with the results of atom-atom potential energy barrier (PB) c culations. tj /s (xlO" C /s" ...

Fig. 7.1.7 Relaxation parameters for contrast in thermal-oxidative aging of SBR. The insets...

All protic solvents undergo multiple relaxation processes due to the presence of hydrogen bonding. In the case of water and formamide (F), the data can be described in terms of two Debye relaxations. For the alcohols and A-methyl-formamide (NMF), three Debye relaxations are required for the description. In all of these solvents, the low-frequency process involves the cooperative motion of hydrogen-bonded clusters. In the case of water and the alcohols the high-frequency process involves the formation and breaking of hydrogen bonds. The intermediate process in the alcohols is ascribed to rotational diffusion of monomers. Studies of dielectric relaxation in these systems have been carried out for the -alkyl alcohols up to dodecanol [8]. Values of the relaxation parameters for water and the lower alcohols are summarized in table 4.5. 

F and NMF are also highly structured solvents as a result of hydrogen bonding. The low-frequency relaxation process in these systems can be attributed to the cooperative motion of hydrogen-bonded clusters. The process at the highest frequencies has a similar relaxation time to those observed in DMF and DMA. Thus, it is probably due to intramolecular rotation about the C-N bond in the monomer. The intermediate relaxation observed in NMF is attributed to rotational diffusion of a monomer. Relaxation parameters for F and NMF are also summarized in table 4.5. 

Table 4.5 Dielectric Relaxation Parameters for Some Protic Solvents at 25°C [5, 9]...

Fig. 18.18. Temperature dependence of the proton relaxation parameters for poled and drawn VDF/TrFE (52/48 mol%) copolymer, showing the ferroelectric transition. The filled triangles correspond to the case where three components for Tip can be resolved. [Reproduced with permission from Ref. 99.]...

Spin polarization conservation effects during triplet-triplet energy transfer in fluid solution has been observed by time-resolved ESR spectroscopy using the pyridinyl radical dimer and a sensitizer. 60 relaxation parameters for spin orbit coupling... 

Relaxation Parameters for the Thermal Vibrational Distribution of States of Benzene in 10-20 torr of Vapor near JOO°K... 

A comparison of dielectric and viscoelastic relaxation a process has its own set of difficulties because the viscoelastic processes are small and the parameters and highly temperature dependent. Nevertheless, the data can be analyzed and comparisons made. A comparison of the relaxation parameters for the a processes of poly(vinyl chloride),... 

Fig. 2. Theoretical values of the NMR relaxation parameters for P at 40.5 MHz. The relaxation parameters were calculated assuming the free internal difiiision model presented in the text with an internal motion correlation time and an isotropic slower motion correlation time T . The calculations include contributions from chemical-shift anisotropy (CSA) as well as dipolar contributions from three protons at a distance of 2.86 A fiom the phos]4iorus. The dipolar interaction is modulated by internal rotation with an angle of 40° between P-H vectors and the axis of internal motion. The CSA contributions utilized the following values chemical shift anisotropy 4= 103 ppm, asymmetry parameter 17 = —0.63 ppm, and Euler angles p = 90°, y = 0°. The off-resonance NMR relaxation parameters and R were calculated assuming a radiofrequency (rf) field of strength 0.48 G applied 8.0 kHz off-resonance. The various curves were calculated assuming values listed next to the curves. From Bolton et al. (1982). Copyright 1982 American Chemical Society.

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