Motion tumbling

Fortunately, the worst broadening interactions are also removed naturally in most liquids and solutions, or at least greatly reduced in their effect, by the tumbling motions of the molecules, for many of the broadening... 

Fig. 16.2 A simplified scheme of the trNOE concept. The ligand L in the free state has negligible cross-relaxation between protons Hi and H2 because of its rapid tumbling motion. Upon binding to the much slower tumbling protein 7 becomes effective and leads to a transfer of magnetization from Hn to H2. Because of the dynamic equilibrium the ligand is released back into solution where it is still in the magnetization state corresponding to the bound form. The same concept is also applicable to trCCR and trRDC (see Sects. 16.4 and 16.5).

As mentioned in Section III.C, it was realized early on that for Gd(III) agents, a significant gain in relaxivity could be obtained by slowing down the tumbling motion (increasing tb) of the metal complex (10). 

The HNMR spectra of the diaqua and aqua (hydroxo) hemin complexes encapsulated in micelles have been reported [20] (Fig. 5). The heme methyl resonances in the diaqua species lie in the same region as those of the high-spin bis(dimethyl sulphoxide) iron (III) porphyrin complex [37-39], while those of the aqua (hydroxo) complex appear in a more upheld region. The positions and linewidths of the heme methyl resonances in these complexes are similar to those observed in the aqua and hydroxo hemoproteins [19,40]. The broadness of the ring methyl resonances of both the diaqua and aqua (hydroxo) species in micelles has been ascribed to arise from the hindered rotational tumbling motion of the heme inside the micelles. The spread and linewidth of these resonances are much larger than those of similar high-spin model heme complexes in simple solution [3]. 

For a particle without fore-and-aft symmetry, condition (ii) is generally met only when the axis is vertical hence such particles fall with a tumbling motion. However, if the particle has fore-and-aft symmetry of shape and density, both F ) and immersed weight must act through the point where the plane of symmetry cuts the axis condition (ii) is automatically satisfied, and the particle falls without rotation. Condition (i) then determines the direction of motion. The angle (p becomes the inclination of the axis from the vertical, so that the... 

Lee et al. evolved a comprehensive analytical-theoretical treatment, based on the solution of the reorientational isotropic diffusion equation, for an ensemble of high-spin systems under motion. These authors developed an analytical expression for the slow-tumbling motional region that relates the orientational-motion correlation time t (in s), or the corresponding tumbling rate t, with the step separation bB, of the ESR fine structure of a quartet by Eq. 8,... 

Newitt and Conway-Jones defined (2) pelletization as the process of transforming a wet, solid mass of finely divided particles into dry, spherical bodies by a continuous rolling or tumbling motion. In a broader sense, pelletization is an agglomeration event used in many powder processes, either for ease of handling or to add value to the product. It spans a range of industries that process solid particles into some suitable form, such as metallurgical, chemical, plastics, fertilizer, rubber, food, and pharmaceuticals (3-6). Since spheres have the lowest surface to volume ratio and exhibit... 

One can see from Eq. (3) that the van Vleck dipolar Hamiltonian is the product of a spatial part and a spin part. In liquids, the rapid isotropic molecular tumbling motion, which occurs at frequencies well above the dipolar linewidth, averages the spatial part (1—3 cos2 6tj) to zero, thus nulling the dipolar broadening. In solids, the spins are constrained to vibrate and rotate about their mean positions, resulting in an effective dipolar Hamiltonian which is generally non-zero, and consequently in... 

Unlike the situation with the dipolar interaction, which averages to zero in liquids due to the rapid molecular tumbling motion, the isotropic rotation leaves a residual chemical-shift Hamiltonian ... 

The contribution of the hyperfine interactions to the relaxation rates of the radical depends on whether the dominant contribution comes from the anisotropic (dipolar) or the isotropic (scalar) part of the hyperfine interaction. Usually, the anisotropic contribution predominates because this interaction can be readily modulated by the tumbling motion of the molecule. However, in radicals and radical anions such as the trifluoroaceto-phenone (115,116), the rotation of the CF3 group may modulate the isotropic part of the hyperfine interaction and the scalar relaxation W0 could dominate the dipolar transition W2. In such a case, the authors have pointed out that the sign of the resulting CIDNP will be independent of the sign of the isotropic hyperfine coupling constants. 

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