Motionally narrowed linewidth

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

For all the cases cited above, which represent those data for which a comparison can be presently made, there is a direct connection between the critical molecular weight representing the influence of entanglements on the bulk viscosity and other properties, and the NMR linewidths, or spin-spin relaxation parameters of the amorphous polymers. Thus the entanglements must modulate the segmental motions so that even in the amorphous state they are a major reason for the incomplete motional narrowing, as has been postulated by Schaefer. ( ) This effect would then be further accentuated with crystallization. 

In this method, resin samples are swollen with solvent and placed into a standard NMR tube. Spectral data are then collected using conventional sequences and hardware of solution-state NMR. The quality of the NMR data depends on the mobility of the individual nuclei in the sample. This molecular motion can be sufficiently high in order to produce narrow linewidths. The study of these solvent-swollen slurries of the SPS resins is known as gel-phase. 

Analysis of the relaxation time indicates that a narrow linewidth in the H NMR spectra generally implies that the protons on the surftice of M-SbA are mobile, while a wide one indicates that proton motion on the surface of M-SbA is rather restricted. The IR spectra study yield absorption bands at 2800-3200 cm to show the presence of free water in addition to the —OH of Sb-OH (2800-3000 cm ). The peaks attributed to the Sb-OH group decrease markedly with increasing uptake of Li. These results indicate that lithium ion exchange is attributed to the dehydration in the M-SbA structure. 

Lithium-doped BPO4, another candidate ceramic electrolyte material for lithium batteries has been studied by Li NMR relaxation and linewidth measurements of samples with Li doping levels up to 20 mol % (Dodd et al. 2000). Comparison of the NMR data with values of the second moment calculated for both random and homogeneous models of Li distribution indicate the existence of Li clusters with an intemuclear distance of 3A, possibly consisting of 1 Li ion fixed at a boron vacancy with additional 2 Li ions in the conduction channels surrounding the vacancy. The atomic jump time, determined from measurements of the Li motional narrowing behaviour, indicate a maximum in the Li ionic mobility at the 10 mol % doping level (Dodd et al. 2000). 

The criterion for such motional narrowing is Zl- r 1, where A is the static linewidth of the relevant species and ris its motional correlation time. "" We reasonably substitute the... 

The motional narrowing of a resonance occurs when the frequency of motion exceeds the static linewidth and an averaging of the dipole... 

Figure 6.2. The temperature dependence of the H NMR peak-to-peak linewidth AWpp in irans-PA [21,22] x. after [21], The other symbols (2,0 G) O (1,5 G) O (1.3 G) (1.0 G) are taken from [22], where the figures in the parentheses mean the ESR linewidth AWpp at 50 MHz and 300 K. It is remarkable that A//pp is practically independent of the magnitudes of the second moments A/2. The curious behaviour of x symbols was interpreted by the motional narrowing due to chain rotation around the chain axis [21], So far, no successful follow-up of this data has been reported [2,20,22,30],...

Other problems to be resolved, revealed by further exijerimental. studies, are (1) that the temperature dependence of ll NMR T/, yields a temperature variation of the diffusion rate that is inconsistent with the motional narrowing of the ESR linewidth and the DNP results (2) that C NMR does not follow (14) [ 148,150,152,181 ] and (3) that a variety of ESR measurements gave conclusions inconsistent with each other both qualitatively and quantitatively [160, 161,164,165,186]. 

Robinson and co-workers have analyzed ESR TTc as a fimction of temperature measured at 9.5 and 16 GHz and as a function of frequency at rt, as shown in Figure 6.34 [164]. They assumed a model that the mechanism for is the modulation of the electron-electron dipolar interaction due to scattering of the spins by acoustic phonons. They also assumed two levels of diffusion (1) almost free rapid motion within a domain of 50 carbons as proposed by the ENDOR analysis in an unoriented C enriched sample [117], which dominates the ESR 77,. at the X-band and (2) slow migration of such a domain which assures compatibility with the motional narrowing of the ESR linewidth. The rapid diffusion within the domain is not of activation type and the diffusion rate increases with decreasing temperature. On the contrary, the migration is of activation type. However, such an analysis of the ENDOR data [117] was pointed out to be incorrect in section 3.2.5 [105]. Then, it is probable that this model will give rise to some inconsistency with other observations as follows. 

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