Motional narrowing effects

Fig. 5.1.2 Non-ideal capillary flow reactor (a) propagators [13] and (b) corresponding RTDs calculated from the propagator data, (a) The propagators indicate the distribution of average velocities over each observation time (A) ranging from 50 ms to 1 s. As the observation time increases the spins exhibit a narrowing distribution of average velocities due to the motional narrowing effect of molecular diffusion across the streamlines. The dashed vertical line represents the maximum velocity that would be present in the absence of molecular...

Equation (3) has several other important implications which can be directly confirmed by finite-frequency probes. One example is the motion-narrowing effect in NMR experiments which is expected to disappear when l/r is below the chemical-shift-anisotropy (CSA) width. Indeed the NMR results of Tycko et al. [16] indicate that for a CSA width of 18.2 kHz the line broadens below 190 K and develops a powder pattern at lower temperature. This is in fair agreement with the 200 K calculated from Eq. (3). They also concluded that the thermal activation energy is around 260 meV below TV, again close to the values we calculated. The glassy dynamics can be probed by other experiments such as sound attenuation, microwave absorption, and thermal conductivity. In particular the characteristic temperature will depend on probe frequency. Such studies are essential to fully understand the low-temperature orientational dynamics. 

As pointed out in [493], under anisotropic conductors, T T2 and an anisotropic linewidth is observed so that the motional narrowing effect leads to a reduced anisotropic factor (zl//max/ //min) < 2, as observed in all these compounds. 

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. 

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... 

It has recently been demonstrated that the analysis of MAS sidebands patterns can be used to study molecular dynamics in the solid state [85-88]. Indeed, the line narrowing effect of MAS can be partly offset, or completely eliminated, if the 2H quadrupole tensor is reoriented due to motion on a time scale comparable to (first-order quadrupolar broadening, such motion-induced effects should be less evident in the DQMAS spectrum, as has indeed been observed by Wimperis and colleagues in several deuterated solids [87, 88]. For example, the simulation of the SQ spectrum of tetrathionate dihydrate-cfi yielded the same reorientational rate constant as the previously described quadrupolar echo approach (Fig. 6). 

In addition to the effects of motional narrowing, vibrational line shapes for the OH stretch region of water are complicated by intramolecular and intermolecular vibrational coupling. This is because (in a zeroth-order local-mode picture) all OH stretch transition frequencies in the liquid are degenerate, and so the effects of any... 

Herein we present calculations [6] for liquid H20 that are similar in spirit but different in detail from those of Buch [71, 110] and Torii [97]. The MD simulations are of the SPC/E model [135]. Local-mode anharmonic frequencies are generated from our most recent map developed for the H0D/D20 system [98], as are our transition dipoles. The relatively small intramolecular coupling fluctuates with molecular environment, and is determined by a separate map parameterized from ab initio calculations on clusters. The form of the intermolecular couplings is transition dipole, which is tested and parameterized from additional ab initio calculations. The effects of motional narrowing are taken into account approximately with the TAA [99]. 

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). 

In passing it is interesting to note that Fig. 5 qualitatively explains the reason for the difference in the effect of motion on spectral lines in radiofrequency and optical spectroscopy. In radiofrequency spectroscopy one refers to motional narrowing, while collisional broadening is used to... 

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. 

Selected entries from Methods in Enzymology [vol, page(s)] Electron paramagnetic resonance [effect on line width, 246, 596-598 motional narrowing spin label spectra, 246, 595-598 slow motion spin label spectra, 246, 598-601] helix-forming peptides, 246, 602-605 proteins, 246, 595 Stokes-Einstein relationship, 246, 594-595 temperature dependence, 246, 602, 604. 

Since crosslinked polymer networks exhibit anisotropic internal motions, the effect of MAS on the line narrowing is explained assuming that the rigid lattice second moment AM2 consists of two terms, analogous to Eq. (34). Then, the residual line width in the NMR MAS experiment, Acomas, can be described by the following relation ... 

The nuclear Overhauser effect (NOE) is a consequence of the modulation of the dipole-dipole interactions (through space) between different nuclei and is correlated with the inverse sixth power of the internuclear distance. Experimentally, the NOE is the fractional change in intensity of one resonance when another resonance is irradiated in a double-irradiation experiment. The NOE phenomenon is intimately related to spin relaxation. The NOE varies as a function of the product of the Larmor frequency, co0, and the rotational correlation time, tc. In small molecules, tc is short relative to uo"1. In this extreme motional narrowing situation, the frequency... 

Effect of Solvent. With PVAc adsorbed at the A 203-liquid interface, no motionally narrowed component is observed with any solvent, ranging from nearly athermal (CHC- 3) to nearly a theta solvent (CCU) (17.,30). With PVAc(6l,000) at the Ti02-liquid interface, as shown in Figure 5, a small percentage (<5) of very... 

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