Anisotropy widths

In order to obtain further information about the molecular motion of the siloxane chain, the Si powder pattern spectra were recorded [40]. Figure 17.32 shows the Si CP NMR powder pattern spectra for the CPTMPS/DMS copolymer obtained without MAS at -90, 25 and 110°C. These powder pattern spectra predominantly come from the TMPS moiety, because the CP efficiency for the DMS moiety is negligibly small when compared with that for the TMPS moiety as seen from the Si CP/MAS NMR experiments. The anisotropy widths (Tu - <7-331 obtained from the tent-like powder pattern spectrum are 57.8, 55.0 and 52.0 ppm at -90, 25 and 110°C, respectively. The anisotropy width decreases as the temperature is increased. This indicates... 

MAS Si speetnim of a sample of sodium disilieate (Na Si O,) erystallized from a glass is shown as an example. Whilst the statie speetnim elearly indieates an axial ehemieal shift powder pattern, it gives no evidenee of more than one silieon site. The MAS speetnim elearly shows four resolved lines from the different polymorphs present in die material whose widths are 100 times less than the ehemieal shift anisotropy. 

The second-order quadnipolar broadening of tire - transition can be further reduced by spiiming at an angle other than 54.7° (VAS), the width being a minimum between 60-70°. The reduction is only 2 however, and dipolar and shift anisotropy broadening will be reintroduced, thus VAS has only found limited application. 

The widths of the narrow Lorentzians representing slow motions in the plane and perpendicular to the plane of the bilayer are compared in Ligures 11a and 11b, respectively. Lor the in-plane motion, the MD values for Q = 0.5 A agree well with the experimental results, but the increase with Q is significantly overestimated in the simulation compared to the experimental values. This suggests that the slower component of the in-plane motion in the simulation is too fast at short distances. On the other hand, the MD line widths for the slower component of the out-of-plane motion agree well with the experimental results at 30% hydration. As in the case of the LISL, the simulation predicts a slight anisotropy not seen in the experimental data. 

In principle, pulsed excitation measurements can provide direct observation of time-resolved polarization decays and permit the single-exponential or multiexponential nature of the decay curves to be measured. In practice, however, accurate quantification of a multiexponential curve often requires that the emission decay be measured down to low intensity values, where obtaining a satisfactory signal -to-noise ratio can be a time-consuming process. In addition, the accuracy of rotational rate measurements close to a nanosecond or less are severely limited by tbe pulse width of the flash lamps. As a result, pulsed-excitation polarization measurements are not commonly used for short rotational periods or for careful measurements of rotational anisotropy. 

The spectral line widths are related to the rate of the rotational motions, which average anisotropies in the g- and hyperfine matrices (Chapter 5), and to the rates of fluxional processes, which average nuclear positions in a radical. 

Much of the width arises from incomplete averaging of anisotropies in the g-and hyperfine matrices (Chapter 3). For radicals with axial symmetry the parameters of eqn (2.8) depend on Ag = - g , AA, = AiM - A and tr,... 

If the g- and hyperfine anisotropies are known from analysis of a solid-state spectrum, the line-width parameters (1, and yt can be used to compute the rotational correlation time, tr, a useful measure of freedom of motion. Line widths in ESR spectra of nitroxide spin labels, for example, have been used to probe the motional freedom of biological macromolecules.14 Since tr is related to the molecular hydrodynamic volume, Ft, and the solution viscosity, r, by a relationship introduced by Debye 15... 

The widths of the lines in Fig. 3.1 vary because the anisotropies of g and A (to be discussed in Chapter 4) are not completely averaged out when the molecule or ion tumbles in solution. This issue was implicit in the classic work of Bloembergen, Purcell and Pound2a on nuclear spin relaxation and was formulated in a useful way for EPR by Daniel Kivelson and co-workers.2b d As described in Chapter 2, they showed that the widths, in units of Hz, can often be written as a power series in mr with terms up to second-order (a third-order term is sometimes significant) ... 

At either frequency the sensitivity of the instrument is quite remarkable. The exact signal-to-noise ratio depends upon a number of factors including apparent line width (including g and hyperfine anisotropy), ease of saturation, the temperature, and the linear density of the sample in the quartz tube. For a relatively narrow line with peak-to-peak separation of two gauss it is possible to observe the spectrum for concentrations as low as 1014 spins per gram of sample. As the spectrum becomes more anisotropic, the sensitivity of course decreases. Lowering the temperature increases the sensitivity since the population difference An increases [(Eqs. (26) and (3°)]. 

It is quite common to observe that the lines in a nitroxide spectrum show variations in width. One feature which contributes to this is the anisotropy of the nitroxide grouping, as a consequence of which the high field component of the nitrogen triplet may be perceptibly broadened. This effect is particularly noticeable when free tumbling of the nitroxide molecule is restricted either by the viscosity of the solvent or when the radical is incorporated into a very large (e.g. polymer) molecule. This selective line broadening is, of course, one of the principal sources of information in spin-labelling experiments (Berliner, 1976). 

Here, ak is the isotropic chemical shift referenced in ppm from the carrier frequency co0, SkSA is the anisotropy and tfk SA the asymmetry of the chemical-shielding tensor, here also expressed in ppm. Note that for heteronuclear cases different reference frequencies co0 are chosen for different nuclei (doubly rotating frame of reference). The two Euler angles ak and pk describe the orientation of the chemical-shielding tensor with respect to the laboratory-fixed frame of reference. The anisotropy dkSA defines the width and the asymmetry t]kSA the shape of the powder line shape (see Fig. 11.1a). 

The emission anisotropy can be calculated from the experimental decays of the polarized components by means of Eq. (6.43), but only if the decay times are much larger than the width of the excitation pulse. Otherwise, Eq. (6.43) cannot be used because the responses R(t) (= E(t)I(t)) and R (t) (= E(t) 0 I (t)) must be deconvoluted. Several methods can then be used to recover the parameters ... 

The chemical shift 5, defined by Equation (22), was measured at 40.0 and 15.6 Mc./sec. and was found to be —3 2 relative to water for both SA and SG. The derivatives of the resonance absorptions were recorded in the measurements. If the total anisotropy of the chemical shift of protons in the solid is somewhat less than the line width, the cross-over point of the derivative will correspond to the average value of S as for liquids, and will be directly comparable with the shifts for protons in the liquid state. Comparison of the shift value with those of H3O+ (aqueous) (1 1), S = -1-11, OH (aqueous) (121), S = -1-10 dilute solutions of alcoholic-type protons... 

In an organic solid representative broadenings are 150 ppm for aromatic carbon chemical shift anisotropy and 25 kHz (full width at half-height) for a rather strong carbon-proton dipolar interaction. At a carbon Larmor frequency of 15 MHz, the shift anisotropy corresponds to 2.25 kHz. In high magnetic fields the forms of the respective Hamiltonians are... 

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