Motionally-narrowed

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. 

Formulae (3.15)—(3.17) are quite general because the method is indifferent to how the perturbation changes in time. It may be a sequence of collisions or random continuous noise. Thus, the results are valid when the gas is condensed into a liquid. Motional narrowing of rotational structure progresses with increase of density as long as... 

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

Burshtein A. I. Motion-broadened and motion-narrowed spectra, Chem. Phys. Lett. 335 10 (1981). 

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... 

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...

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

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... 

The line broadening caused by partial motional narrowing can be distinguished from that due to isotropic reorientation at a reduced rate by appropriate magic angle spinning experiments. 

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. 

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