Reorientation angles

Inequality (6.67) is the softest criterion of perturbation theory. Its physical meaning is straightforward the reorientation angle (2.30) should be small. Otherwise, a complete circle may be accomplished during the correlation time of angular momentum and the rotation may be considered to be quasi-free. Diffusional theory should not be extended to this situation. When it was nevertheless done [268], the results turned out to be qualitatively incorrect orientational relaxation time 19,2 remained finite for xj —> 00. In reality t0j2 tends to infinity in this limit [27, 269]. 

CODEX analysis based on reorientation angle and difference tensor... 

In Eq. (2), the argument of the cosine function, which depends on 8Ntr and the reorientation angles (aR, fiR, yR), can be considered as the phase acquired within a time of N/2tr under the action of the chemical-shift difference tensor coA = (a>2 - principal values of the difference tensor are WA22 = 0, and the full-width anisotropy coA33 - ouAl, of A, i.e. the range of possible frequency differences, is 20 56... 

This represents a strong linear dependence on the reorientation angle for /3r<45°, which permits relatively easy detection of small-angle motions. 

T = 275 K. The powder spectra olThe deutcrons at different chemical shifts overlap. The material is completely amorphous. The molecular segments undergo reorientation by isotropic lotational diffusion, (e) Distribution of reorientation angles for atactic PP established within the mixing time f ,.. Adapted from Blu4 with permission from Wiley-VC H. 

Fig. 6.2.2. Left Simulated NMR lineshapes that are averaged by various characteristic segmental motions. In the case of fast rotation, y represents the angle between the rotation axis and the C—bond. For a two-site jump, j3 denotes the angle between the C—bond in the two configurations, and the effective asymmetry parameter becomes 17 7 0. Right Calculated 2D exchange spectra for a two-site jump with /3 = 120° (top), and for continuous diffusion (bottom). The distribution functions P(/3) of the reorientation angle are shown, together with the contour maps of the corresponding spectra. All data are displayed on the reduced frequency scale in units of Cq, and mixing times are set equal to the motional correlation time r,..

Four different models of molecular motion were in agreement with the jump angle determined by NMR. However, of these possible motions only one was in agreement with the dielectric relaxation results of Miyamoto et al. [69], This motion is defined by a dipole-moment transition and a conformational change (tg" tg <->g tg" t) yielding an effective dipole-moment reversal only along the chain axis and a reorientation angle of 113° for the C—bond directions. 

TABLE 4 The Time of UV (360 nm) Irradiation, the cis Anisotropy Relative to the trans Anisotropy, and the Reorientation angle a Derived from Relation 20... 

Eight possible isomerizations could occur for the pinned tg + tg- conformation. Four of these isomerizations involved reorientation angles of about 67° or 113° and were consistent with the NMR data. However, each of the four motions implied a different electric dipole moment and only one of these tg + tg- to g-tg + ) was consistent with dielectric data. Therefore, from a combination of NMR data and dielectric data it was possible to uniquely determine the particular mechanism for reorientation of PVF2 although neither of these methods would determine the reorientation mechanism alone. 

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