Motional narrowing, NMR

I. J. Lowe, "Motionally narrowed NMR line shapes in solids" in Magnetic Resonance in Condensed Matter — Recent Developments, Proceedings of the IVth Ampere International Summer School, Pula, Yugoslavia, Sept. 13-23, 1976, edited by R. Blinc and G. Lahajnar (Univ. of Ljubljana, Ljubljana, 1977). 

Andrew and Fades [24] investigated the proton spin resonance spectra and spin-lattice relaxation in polycrystalline benzene (CeHe) in the temperature range between 75 K and 278 K. The second moment (the square of the linewidth) of the proton spin resonance line exhibits a characteristic temperature dependence (Fig. 5.19) at T< 80 K the width of the motionally-narrowed NMR line is independent of the temperature. In the range between 80 K and 120 K, the resonance line becomes less broad due to motional narrowing. At T> 120 K, the narrow linewidth again becomes temperature independent. 

NMR studies on graphite-phosphoric acid showed simultaneous, motional narrowing of both H and resonances above 225 K, indicating high mobility of phosphoric acid in the compound (FS). Chloro-sulfonic acid is inserted alone into graphite in the presence of many inorganic chlorides. The reaction temperature and stage seem to be related to the redox potential of the M"+-M couple (M3). 

Lowering the temperature has a similar effect on the deuterium spectra as does increased loadings. In Figure 3, spectra for benzene-d6/(Na)X at 0.7 molecules/supercage over the temperature range 298 to 133 K are shown. It is observed that both benzene species are detected simultaneously between 228 and 188 K. Below this temperature the oriented benzene species becomes the predominant form. A similar situation occurs for polycrystalline benzene-dg in which two quadrupole patterns, one static and the other motionally narrowed due to C rotation, are observed to coexist at temperatures between 110 and 130 K (7). This behavior has been attributed to sample imperfections (8) which give rise to a narrow distribution in correlation times for reorientation about the hexad axis. For benzene in (Na)X and (Cs,Na)X such imperfections may result from the ion/benzene interaction, and a nonuniform distribution of benzene molecules and ions within the zeolite. These factors may also be responsible for producing the individual species. However, from the NMR spectra it is not possible to... 

An interesting application of the motional narrowing concept arises in the double NMR technique BS). In this technique the contribution to the NMR line width of nuclei (A) in a solid by the dipolar fields of dissimilar nuclei (B) may be removed by application of a sufficiently strong rf field at the resonance frequency of the B nuclei. With Hib A/Ib, A/Ia where AH is the line width, flipping of B nuclei by the Hib field will cause fluctuations in the dipolar fields of B nuclei at the A nuclei which are rapid compared to T2a and hence cause narrowing of the NMR line of the A nuclei. This effect has been observed in several different solids of the AB type 5S,6A). 

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. 

The application of nuclear magnetic resonance (NMR) spectroscopy to polymer systems has contributed to significant advances in understanding of their structure and dynamical properties at the molecular level. From the analytical point of view, NMR spectroscopy is particularly suitable for a determination of the polymer structure by direct observation of the protons and carbons in different structural moieties. However, until the mid-1970s the application of this technique was limited to polymer solutions and to some elastomers in the solid state with a relatively high degree of the molecular mobility which allows the observation of the motionally narrowed absorption signals. 

Solid-state 13C NMR spectra of carbon black filled, uncured and sulfur-vulcanised HR were recorded at 22.6 MHz. The line broadening of the filled polymer relative to the unfilled polymer is attributed to incomplete motional narrowing of the NMR lines [53, 54] Incorporation of filler also results in a decrease in the signal-to-noise ratios in the spectra, but fundamentally it does not obscure the qualitative and quantitative nature of the spectra for the moderately cured elastomer systems. 

Direct evidence for a spin density wave transport is the detection of a current oscillating at a frequency that is proportional to the dc current carried collectively. The recent observation of such oscillations the harmonic and subharmonic locking of this oscillation to an external ac source and a motional narrowing of the NMR spectrum in the sliding SDW state have established firm evidence for the existence of a novel collective transport in a SDW condensate. 

The period of the pinning SDW potential has been derived from two sets of NMR experiments which have been performed recently in a sliding SDW state. First, measurement of the SDW velocity from the proton spin echo amplitude of (TMTSF)2PF6 [119] (Fig. 37) as a function of the dc current (above threshold field) and comparison with the SDW noise spectrum lead to a pinning potential period that is half the SDW wavelength (namely, a = 2). Second, the result a = 1 is inferred from a study of the amplitude of the motionally narrowed 13C spectrum in (TMTSF)2PF6 and of a SDW current and noise spectrum [111] (Fig. 38). 

According to the discussion in Section 1.1.1.1, a broad Pake spectrum is observed for low mobile PDMS chain units, whereas a narrow line is recorded if the frequency of chain motions exceeds 10 kHz-1 MHz. The effect of hydrophilic and hydrophobic Aerosil on the chain motion is remarkably different. For PDMS filled with hydrophilic Aerosil, a broad H NMR line is observed over the whole temperature range studied. The motional narrowing is not complete, even at 433 K, nearly 300 K above the fg of PDMS. This means that mobility of PDMS chain units at the surface of hydrophilic Aerosil is hindered by adsorption interactions even at 433 K, although the strength of adsorption interactions decreases with increasing temperature. On the other hand, PDMS chains at the surface of hydrc hobic Aerosil are already desorbed at about 200 K, since the NMR line is completely narrowed at this temperature as shown in Fig. 12. 

The narrowing of the viscoelastic spectrum as salinity increases is analogous to motional narrowing of line widths in NMR spectroscopy. The narrowing process occurs when the breakage time Tbr becomes smaller than the reptation time Trep. In the limit Tbr Trep, the Gates model predicts that G(t) is monoexponential, with a time constant t given by... 

The x-ray results presented here show both consistencies and discrepancies with NMR observations. The most serious discrepancy is the implied coexistence of static and mobile C nuclei well below our Tc, deduced from the NMR observation of superposed motionally narrowed and powder pattern signals at temperatures as low as 140 K. On the other hand, a minimum in 7 i at 233 K is observed in one NMR experiment. In fact, the two techniques probe different aspects of the structure. NMR experiments to date cannot distinguish between free rotation and jump rotational diffusion between symmetry-equivalent orientations. X-ray diffraction is sensitive to orientational order (as a canonical average of snapshots) even in the presence of substantial thermal disorder, as long as one set of orientations is statistically preferred and the orientational order is long range. Indeed, our measurements indicate that much of the sc order is reduced by orientational fluctuations at Tc. 

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