Hopping reorientation

Indisputable advantage of the kinematic approximation in comparison with the MMDCR is its applicability to any m. It may be ised to connect the results, relating to the hopping and diffusion approach. It has been done in /9/ for hopping reorientation of the anisotropic reagents. It is clear from the foregoing that this result establishes the lower limit of w, when the rate of the reorientation 1/r is finite. The upper limit is determined by the rotational... 

As indicated, the power law approximations to the fS-correlator described above are only valid asymptotically for a —> 0, but corrections to these predictions have been worked out.102,103 More important, however, is the assumption of the idealized MCT that density fluctuations are the only slow variables. This assumption breaks down close to Tc. The MCT has been augmented by coupling to mass currents, which are sometimes termed inclusion of hopping processes, but the extension of the theory to temperatures below Tc or even down to Tg has not yet been successful.101 Also, the theory is often not applied to experimental density fluctuations directly (observed by neutron scattering) but instead to dielectric relaxation or to NMR experiments. These latter techniques probe reorientational motion of anisotropic molecules, whereas the MCT equation describes a scalar quantity. Using MCT results to compare with dielectric or NMR experiments thus forces one to assume a direct coupling of orientational correlations with density fluctuations exists. The different orientational correlation functions and the question to what extent they directly couple to the density fluctuations have been considered in extensions to the standard MCT picture.104-108... 

Study the dissociation dynamics of such a system, the development of simple models can best be accomplished using semiclassical or classical techniques. In Section IV C a curve-hopping model is developed, based on a collisional reorientation of the electronic angular momentum. It assumes that a bath atom collides with just one of the diatoms and reorients its electronic angular momentum on a time scale that is short compared to the relative motion of the diatoms. The model is applied to iodine photodissociation dynamics in Section IV D. The dissociation dynamics of polyatomic systems with their internal degrees of freedom is more complex than for diatomics. If these degrees of freedom are not thermally equilibrated and are coupled to the dissociation coordinate, then their dynamics cannot simply be projected out, but rather they can act as an indirect source of excitation of the dissociation coordinate. 

As it was pointed out in the Introduction, the problem of the coexistence of displacive and order-disorder phenomena at the ferroelectric phase transitions of BaTiOs has met growing interest in recent time. Strong support of the order-disorder model comes 30 years ago from EPR measurements performed on Mn" " "-, Cr -, and Fe -doped BaTiOs [218-222] because in the low-temperature rhombohedral phase it was observed that Mn" " ", which substitutes isovalent Ti" " " sites, is displaced off-centre by 0.14 A along <111> directions with a reorientational hopping with correlation times 10 -10 s. 

The proton, although it is very small, has a veiy high molar conductivity (Table 21.6) Proton and NMR show that the times characteristic of protons hopping from one molecule to the next are about 1.5 ps. which is comparable to the time that inelastic neutron scattering shows it takes a water molecule to reorientate through about I rad (1—2 ps). 

The primary difference between solid-state and liquid-state NMR is one of time scale. The atomic dynamics of the sample define a natural internal time scale, denoted t. The motion of interest might be, for example, the rotational tumbling of molecules in a liquid, the reorientation of segments in a polymer, or the hopping of ions in a solid electrolyte. Clearly, t can range from picoseconds to seconds or more. As... 

Figure 7 Two-dimensional exchange spectrum of deuterated dimethylsulfoxide. The strong diagonal ridge reflects molecules that have not reoriented during the mixing time, while the pattern of ellipses off the diagonal shows those that have. The ellipses arise due to the orientational dependence of the quadrupole interaction, the dominant anisotropy here. The distribution of jump angles is shown on the right, and sharply peaked at zero (static molecules) and 72°, the included angle of the C-D bonds as the entire molecule executes hops about its symmetry axis. With this type of experiment, slow to moderate dynamics of molecules and polymers can be followed in atomic level detail. (Reproduced with permission from Schmidt-Rohr K and Spiess HW (1994) Multidimensional Solid-Stale NMR and Polymers. London Academic Press.)...

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