Anisotropy of the chemical shift

We have referred to the various interactions which can cause line broadening in the solid state. One of these, which is normally not a problem in liquid state NMR, is due to the fact that the chemical shift itself is a tensor, i.e. in a coordinate system with orthogonal axes x, y and z its values along these axes can be very different. This anisotropy of the chemical shift is proportional to the magnetic field of the spectrometer (one reason why ultra-high field spectrometers are not so useful), and can lead in solid state spectra to the presence of a series of spinning sidebands, as shown in the spectra of solid polycrystalline powdered triphenylphosphine which follows (Fig. 49). In the absence of spinning, the linewidth of this sample would be around 75 ppm ... 

Although anisotropy of the chemical shift is expected for nuclei in non-cubic symmetry, the average value obtained for a polycrystalline solid should be comparable to these shifts for liquids, which are also average values. The chemical shift for concentrations of fluorine in the intermediate and on the high part of the concentration range of the samples examined was found to be (—40 40 ppm) relative to F (aqueous). No large shift for the fluoride ion occurs in the solids examined compared to the heavier halides in the solid state 118), indicative of the ionicity of the A1—F bond involved. 

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... 

Solid-state NMR spectra of V20s/Sn02 catalysts and pure V2O5 alone are shown in Figure 2. Two types of distinct signals, with varying intensities depending on the vanadia content on tin oxide support, are the main features of these spectra. Unsupported and crystalline pure V2 Os exhibits a line with an axial anisotropy of the chemical shift tensor ( = -310 ppm and 6 = - 1270 ppm) with small peaks due to... 

The isotropic chemical shift is the average value of the diagonal elements of the chemical shift tensor. Advances in solid state NMR spectroscopy allow one to determine the orientation dependence, or anisotropy, of the chemical shift interaction. It is now possible to determine the principal elements of a chemical shift powder pattern conveniently, and the orientation of the principal axes with more effort. Hence, instead of settling for just the average value of the chemical shift powder pattern, one can now aim for values of the three principal elements and the corresponding orientations in a molecular axis system. 

FIGURE 12. Bottom 13C NMR line shapes of 7Li bound 13C, 1./ (13C,7 Li) = 43.3 Hz, subject to relaxation via anisotropy of the chemical shift, csa, at different rates, jc Top as above, but calculated as a function of the dipole-dipole (dd) relaxation rate, vi- Reprinted with permission from Reference 14. Copyright (1995) American Chemical Society... 

The sample is placed into a gas driven spinner, the rotation axis of which is inclined by an angle ij/ against the magnetic field Bo (Fig. 3.3.4). For MAS this angle is adjusted to the magic angle of 54.7°. Then the anisotropic parts of all interactions which are described by second-rank tensors can be averaged. These are the anisotropy of the chemical shift, the dipole-dipole interaction, and the first-order quadrupole interaction. 

To measure high-resolution spectra of disordered samples, the anisotropy of the chemical shift must be eliminated in addition to the homonuclear dipole-dipole interaction. This can be achieved for abundant nuclei by combined rotation and multi-pulse spectroscopy (CRAMPS), which is the combination of homonuclear multi-pulse spectroscopy and MAS [Bur2, Ger2, Sch6]. In Fig. 3.3.13, H spectra of monoethyl fumarate are compared for different NMR techniques [Brol]. Only the combination of MAS and multi-pulse excitation produces a high-resolution spectrum of the polycrystalline powder. 

Table 1. Tensor elements for the estimated anisotropy of the chemical shift interaction for characteristic CH -groups of cetyl palmitate. The values derive from n-eicosane and polyethylene...

Under anisotropic conditions, NMR lineshapes for a quadrupolar nucleus are dominated by chemical shielding and (first and second order) quadrupolar interactions. Dipolar interaction is usually a minor contribution only. First-order quadrupole interaction lifts the degeneracy of the allowed 21 (i.e. seven in the case of V / = V2) Zeeman transitions as shown in Figure 3.7, giving rise to seven equidistant lines, viz. a central line (mj = + V2 -V2. unaffected by quadrupole interaction) and six satellite lines. The overall breadth of the spectrum is determined by the size of the nuclear quadrupole coupling constant Cq the deviations from axial symmetry and hence the shape of the spectral envelope are governed by the asymmetry parameter. Static solid-state NMR thus provides additional parameters, in particular the quadrupole coupling constant, which correlates with the electronic situation in a vanadium compound. [ 1 The central component reflects the anisotropy of the chemical shift. 

Compared with the crystalline phase, isotropic chemical shifts of the amorphous phase appear at high frequency by about 1 ppm. Anisotropy of the chemical shift tensor for the amorphous phase is much less than that for the crystalline phase. Tight binding MO calculations are carried out for polyoxymethylene by changing the dihedral angle (4>) (Fig. 7.12) [22]. As... 

A pioneering work on the WAHUHA multiple-pulse sequence applied to F NMR of a fluorinated polymer was reported by Ellett et al. [116]. They obtained resolved chemical shifts for the OCF3 and CF2 peaks (separation 73 ppm) of a copolymer of 60/40 TFE and perfluoromethylvinyl ether. Good agreement between the area of the peaks and the known composition of the copolymer was obtained. The anisotropy of the chemical shift of the CF2 groups was approximately determined. 

Detailed information about the electronic structure of the silicon-silicon double bond was obtained from the 29Si solid state powder pattern spectrum80 of tetramesityldisilene. The anisotropy of the chemical shift of Si=Si was found to be comparable to that of C=C in ethylene. In contrast, the anisotropy of Si-Si in the analogous tetramesityldisilane was found to be small which is characteristic of alkanes as well. Based on the similarities of the chemical shift anisotropies it was concluded that the electronic structure of Si=Si closely resembles that of C=C. 

Figure 14 Chlorine NMR spectra of solid powdered BaCl2 2H20 obtained at 11.75 and 21.1 T. Spectra acquired under MAS and static conditions for both C1 and are shown. Simulated spectra are shown above the experimental spectra. Also, spectra of stationary samples (top) have been simulated with the span of the CS tensor set to zero (see parts E, J and O) to demonstrate the importance of the anisotropy of the chemical shift tensor in obtaining accurate fits. Reproduced by permission of Wiley-VCH from Ref. 112.

The next section explains how the effects of the anisotropy of the chemical shift and of this interaction between spins can be removed. 

The effects of the anisotropy of the chemical shift and of the spin-spin interaetions in the spectra of solids can be eliminated by the use of a teehnique ealled magic-angle spinning (MAS). Equation (2.9) shows that the frequeney of the transition for a particular spin S2 interacting with another spin Si can be written... 

For dilute spins, such as and 31p, the dipolar broadening can be removed by sufficiently intense rf irradiation at the proton resonance frequency.2-4 Nevertheless, a substantial broadening due to the anisotropy of the chemical shift remains. In order to obtain "high resolution" NMR spectra, it has become customary to subject multllamellar dispersions to prolonged ultrasonic irradiation.5 This process, which results in particles of reduced size with reduced reorientational correlation times, does indeed improve the resolution of the NMR spectya however, its exact physical and chemical consequences are a subject of much debate.6 We describe below a method whereby high resolution spectra can be obtained without resorting to sonication. 

Cesium ( Cs) (/=7/2). The cesium-loaded zeolites were systematically studied by Cs NMR and ESR as a function of loading level. The primary Cs NMR signal in Cs-loaded LiA at low loading was assigned to Cs in the eight-ring S II sites and showed axial anisotropy of the chemical shift and those of Cs-loaded LiX and LiLSX were isotropic and... 

The orientation dependence or anisotropy of the chemical shift can be quite dramatic. For a non-sp -hybridized atom, the CSA can be as large as 120-... 

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