Dipolar-dephasing relaxation times

The relaxation parameters, Ti, dipolar-dephasing relaxation times (Tdd), etc. can provide useful information on the dynamics of polymer motion in the solid state and to monitor solid-state polymer phase transitions. 

Fig. 9.10. Intensity of amorphous peaks of samples of PESL and MQPESL versus delay time T [18]. The peak intensity was obtained from computer simulation of the C partially relaxed dipolar-dephasing NMR spectra.

The difference of relaxation times in different domains makes it possible to observe the spectrum of one of the domains. Figure 10.23(a), shows the Ti-selected spectrum of PVPh/PEO = 40/60 [34]. Since the Ti of crystalline PEO ( 15 s) is much longer than that of the amorphous phase (—0.1 s), it is possible to observe the spectrum of crystalline PEO selectively (indicated by arrow in Fig. 10.23(a)). On the other hand, for the miscible PVPh-rich blend (PVPh/PEO = 58/42), the crystalline-PEO peak is not appreciable. This is in agreement with the above-mentioned results (Table 10.2). The signals of mobile domains/component polymers can be observed selectively by utilizing the weaker dipolar interaction between H. To name a few examples, the dipolar dephasing [128,131,152], the cross-polarization-depolarization [152] and the pulse saturation transfer [151] techniques have been applied. 

For the 13C CP/MAS measurement and dipolar-dephasing CP/MAS NMR the experimental conditions were 3 ms contact time, 5 s repetition time, 40 kHz spectral width, and 8 k data points. The l3C chemical shifts were calibrated through the hexamethylbenzene peak (17.3 ppm relative to tetramethylsilane). The l3C relaxation measurements were performed with Torchia s pulse sequence."... 

The applications of solid-state C-NMR spectra for the study of polymorphs and solvates can go beyond evaluations of resonance band positions and make use of additional spectral characteristics. For instance, studies of relaxation times of furosemide polymorphs were used to show the presence of more molecular mobility and disorder in Form II, while the structure of Form I was judged to be more rigid and uniformly ordered [158]. The analysis of the solid-state C-NMR spectra of (li ,3 j-3-/ -thioanisoyl)-l,2,2-trimethylcyclopentanecarboxylic acid was facilitated by the 7-modulated spin-echo technique, which was used to deduce the number of protons bound to each carbon atom [159]. Differences in the dipolar dephasing behavior between the two polymorphs of ( )- ra 5-3,4-dichloro-A/-methyl-7V-[ 1,2,3,4-tetrahydro-5-methoxy-2-(pyrrolidin-1 -yl)]naphth-1 -yl-benzeneacetamide were noted and ascribed to motional modulation of the carbon-hydro-... 

Reff = observed dipolar coupling constant t = time T20 = spin term in the spherical tensor representation of the dipolar Hamiltonian = zero-quantum relaxation time constant U = propagator = magne-togyric ratio of spin / A/ = anisotropy of the indirect spin-spin interaction 0 = angle between the applied field and the internuclear vector A = dephasing parameter /Uq = permeability of free space Vj. = rotor frequency in Hz 1/, = isotropic resonant frequen-... 

Figure 5 (A) Plots of non-crystalline spin-lattice relaxation times T, of PE-SL samples ( ) and MQ-PE-SL (O) versus the reciprocal absolute temperature. (B) Intensity of non-crystalline peaks of a sample of PE-SL and MQ-PE-SL versus delay time r. The peak intensity was obtained from computer simulation of the partially relaxed dipolar-dephasing NMR spectra. Reproduced with permission of John Wiley Sons from Chen Q, Yamada T, Kurosu H, Ando I, Shioino T and Doi Y (1992) Journal of Polymer Science, Part B Polymer Physics 30 591.

T] = spin-lattice relaxation time T2 = spin-spin relaxation time Tip = spin-lattice relaxation time in the rotating frame DD = dipolar dephasing relaxa tion time. 

The faithful representation of the shape of lines broadened greatly by dipolar and, especially, quadrupolar interactions often requires special experimental techniques. Because the FID lasts for only a very short time, a significant portion may be distorted as the spectrometer recovers from the short, powerful rf pulse. We saw in Section 2.9 that in liquids a 90°, t, 180° pulse sequence essentially recreates the FID in a spin echo, which is removed by 2r from the pulse. As we saw, such a pulse sequence refocuses the dephasing that results from magnetic field inhomogeneity but it does not refocus dephasing from natural relaxation processes such as dipolar interactions. However, a somewhat different pulse sequence can be used to create an echo in a solid—a dipolar echo or a quadrupolar echo—and this method is widely employed in obtaining solid state line shapes (for example, that in Fig. 7.10).The formation of these echoes cannot readily be explained in terms of the vector picture, but we use the formation of a dipolar echo as an example of the use of the product operator formalism in Section 11.6. 

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