Bonds, rotational relaxation

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

These authors also reported theoretical calculations of this frequency-dependent rotational relaxation. The theory of Auer et al. [98] using the quadratic electric field map, originally developed for HOD/D2O, was extended to the H0D/H20 system [52]. As before [38], the orientation TCF was calculated for those molecules within specified narrow-frequency windows (those selected in the experiment) at t = 0. TCFs for selected frequency windows, up to 500 fs, are shown in Fig. 8. One sees that in all cases there is a very rapid decay, in well under 50 fs, followed by a pronounced oscillation. The period of this oscillation appears to be between about 50 and 80 fs, which corresponds most likely to underdamped librational motion [154]. Indeed, the period is clearly longer on the blue side, consistent with the idea of a weaker H bond and hence weaker restraining potential. At 100 fs the values of the TCFs show the same trend as in experiment, although the theoretical TCF loses... 

Absorption of a photon by an alkene produces a (tt,Jt ) vertical (Franck-Condon) excited state in which the geometry of the ground state from which it was formed is retained. Since the (it,it ) state has no net n bonding, there is little barrier to free rotation about the former double bond. Thus, relaxation takes place rapidly, giving a nonvertical (it,it ) state with a lower energy and different geometry to the vertical excited state. 

It is clear that the function U ( qint ) tmy be approximated by an expression of the form of eqn. (6). Whether a potential of Ais form, involving no explicit description of the solvent, is appropriate depends on the relative relaxation rates of the solvent motions and the macromolecular intramolecular coordinates. For the slow, conformationally most significant, glycosidic and exocyclic bond rotations of the carbohydrate it is apparent Aat averaging of solvent motions can occur easily on the time scale of these torsions. It is more ficult, however, to know how much important conformational detail is submerged by the averaging process. 

The geometric relaxation described in Section 12.3.1 occurs by redistributing the bond valence between the bonds until GII and BSI both have acceptable values, but in some cases this relaxation is restricted by symmetry. In the case of per-ovskite, the cubic symmetry of the archetypal ABO3 structure (Fig. 10.4) does not allow any of the bonds to relax unless the symmetry is lowered. Thus true cubic perovskites are rare since they can only exist if the A and B ions are exactly the right size. Most perovskites have a reduced symmetry that allows the bonds to relax. For compounds in which the A-O bonds are stretched, the relaxation takes the form of a rotation of the BOg octahedra and results in a reduction of the coordination number of A. The various relaxed structures based on different expected coordination numbers were modelled in Section 11.2.2.4. 

The nmr data for this type of motion are direct and the motion clearly involves rotation about bonds in the millisecond time scale range. However. less direct evidence for motion comes from other techniques such as fluorescence depolarization, 02 diffusion, hydrogen exchange kinetics, and nmr relaxation times (see Ref. 4). The extent of this motion is not yet easy to define, but this evidence points to motion in the nanosecond time scale range. It is tempting to see the motion in this time scale as bond oscillations rather than rotations. To put it in a different way, on this time scale the side chains have some freedom to move with respect to each other but not normally to undergo substantial bond rotation. Table IV summarizes some references for motion of different types. Additionally, nmr relaxation studies suggest that the backbone or main chain of a protein is more restricted than that of the side chains. 

The rotational relaxation of low-viscosity solvents takes place in times of ps. This can be observed through time-resolved spectroscopy when the dipole moment of the excited molecule differs substantially from that of the ground state species. Table 8.2 gives a few values of these relaxation times the alcohols show rather slow relaxation because of the hydrogen bonds which associate the solvent molecules. 

Despite the simplicity of this molecule and its symmetry, significant changes in the Si-O bond torsions occur when adjacent bonds are relaxed. A comparison between the results of the standard method and the new scanning method is shown in Figure 4. For this particular case, rotation of one methyl group around the Si-C bond is not sensitive to the variation of... 

The impact of bath molecules on the atoms of the molecule of interest cannot be treated as impulsive because the strong binding forces of chemical bonds places a significant fraction of the vibrational sjjectrum of the molecule above the collisional bandwidth, broadly defined as the reciprocal of the duration of a collision. Thus collisional vibrational relaxation and excitation are inefficient relative to rotational relaxation. Binary collision theory is well develojjed at the microcanonical level because of the its importance in chemical reactions. The relationship to the friction is of interest, " primarily because stochastic treatments have the potential of bridging the gas-phase limit of resolved binary collisions and the liquid phase where collective phenomena of the solvent can preclude interpretation in terms of binary collisions. 

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