Anisotropy reorientation

Chemical shift anisotropy (CSA) 2 Reorientation of the CSA principal axis Increases with the square of the magnetic field [13]... 

Hochstrasser R M ef a/1991 Anisotropy studies of ultrafast dipole reorientations Proc. Indian Acad. Sc/. (Chem. Sci.) 103 351-62... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Another important linear parameter is the excitation anisotropy function, which is used to determine the spectral positions of the optical transitions and the relative orientation of the transition dipole moments. These measurements can be provided in most commercially available spectrofluorometers and require the use of viscous solvents and low concentrations (cM 1 pM) to avoid depolarization of the fluorescence due to molecular reorientations and reabsorption. The anisotropy value for a given excitation wavelength 1 can be calculated as... 

The previous approach is valid as long as the molecular reorientation can be described by a single correlation time. This excludes molecules involving internal motions and/or molecular shapes which cannot, to a first approximation, be assimilated to a sphere. Due to its shape, the molecule shown in Figure 15 cannot evidently fulfil the latter approximation and is illustrative of the potentiality of HOESY experiments as far as carbon-proton distances and the anisotropy of molecular reorientation are concerned.45 58... 

Figure 15 The model molecule used to demonstrate the possibilities of HOESY experiments in terms of carbon-proton distances and reorientational anisotropy. To a first approximation, the molecule is devoid of internal motions and its symmetry determines the principal axis of the rotation-diffusion tensor. Note that H, H,., H,-, H,/ are non-equivalent. The arrows indicate remote correlations.

The overall tumbling of a protein molecule in solution is the dominant source of NH-bond reorientations with respect to the laboratory frame, and hence is the major contribution to 15N relaxation. Adequate treatment of this motion and its separation from the local motion is therefore critical for accurate analysis of protein dynamics in solution [46]. This task is not trivial because (i) the overall and internal dynamics could be coupled (e. g. in the presence of significant segmental motion), and (ii) the anisotropy of the overall rotational diffusion, reflecting the shape of the molecule, which in general case deviates from a perfect sphere, significantly complicates the analysis. Here we assume that the overall and local motions are independent of each other, and thus we will focus on the effect of the rotational overall anisotropy. 

In a totally independent approach, highly fluorescent but rigid molecules can be used and their reorientational movement probed in solution, mostly by time-resolved fluorescence anisotropy, (85) For rodlike molecules likep-oligo-phenyls, this movement corresponds to the reorientation of the long molecular axis the length of which can be easily varied. 86 The use of fluorescence probes in liquid and solid media and on surfaces has been treated recently in several reviews and books. 87 ... 

It can be seen that, in all cases, relaxation rates are directly proportional to (Aa). Because Aa reflects the anisotropy of the shielding tensor and because the chemical shift originates from the shielding effect, the terminology Chemical Shift Anisotropy is used for denoting this relaxation mechanism. Dispersion may be disconcerting because of the presence of Bq (proportional to cOq) in the numerator of and R2 (Eq. (49)). Imagine that molecular reorientation is sufficiently slow so that coo 1 for all considered values of coo from (49), it can be seen that R is constant whereas R2 increases when Bq increases, a somewhat unusual behavior. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

The Orbach-type process as well as the collisional process (inducing either ZFS, g anisotropy or hyperfine coupling modulation) are mechanisms that can provide electron relaxation independently on reorientation. Electron relaxation is certainly not modulated by reorientational motions... 

The dynamic simulation of crystals at equilibrium is quite feasible [64] and gives information on molecular detail like the anisotropy of librations, or the frequency of molecular reorientations. Second-order phase transitions are also within scope. 

The excellent resolution of the 0-tensor components at W band has been used to measure the relaxation properties of QA in the Zn-substituted bRC of R. sphaeroides.m The experiment showed, in contrast to the respective ubiquinone radical in organic solution, an anisotropic relaxation behavior in the pulse high field ESE experiments. From the analysis of the T2 experiments a motional anisotropy of Q% in the protein pocket was deduced with a preferred libration about the C-O symmetry axis. Recently, similar experiments were also performed on Qb- in ZnbRCs. Compared to QA different echo decay time constants were found. A model was proposed in which the relaxation is related to reorientational fluctuations around the quinones specific H-bonds to the protein.142... 

Fig. 4.20. The influence of the tunnelling recombination anisotropy upon the non-steady-state luminescence kinetics. Curves 1 and 2 correspond to the defect reorientation switching-on and -off, respectively at the moments given by broken lines [106],...

Grabko et al. (1977) studying the anisotropy of the mechanical properties of admixed ZnTe monocrystals used the scratch method to reveal the reorientation of blocks in crystals ZnTe Mg, and ZnTe Be (Fig. 4.3.7). The minimum-hardness direction within one block would change... 

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