Dipolar shielding tensor

Nuclear magnetic resonance (NMR) is a technique of considerable versatility in polymer science. It is used universally as a probe of chemical configurations, it provides information on the dynamics and relaxation times of a polymer system and it offers a route to the determination of orientation parameters, the exact route depending on the particular nuclei employed. In principle quadrupolar, dipolar, shielding tensor and indirect spin coupling interactions can all be employed " however, in practice only the first two have any universal appeal. Dipolar coupling using proton NMR offers the simplest approach in terms of material preparation and will be considered first. 

Composite-pulse decoupling schemes like WALTZ [36, 37], DIPSI [38], or GARP [39], which are used in solution-state NMR, have failed to offer any significant improvements in the solid state compared to CW decoupling. The residual line width in CW-decoupled spectra is dominated by a cross term between the chemical-shielding tensor of the protons and the heteronuclear dipolar-coupling tensor [40, 41]. 

As with dipolar relaxation, the interaction energy for CSA (in this case from Eqs. 6.3 and 7.17) enters quadratically, leading to the following expression for an axially symmetric shielding tensor in the extreme narrowing limit ... 

Fig. 5. (a) Two-dimensional 1SN- H dipolar/chemical shift spectrum obtained from [lSN]acetylvaline showing the dipolar and chemical shift projections. Linewidths are typically 50-150 Hz for the dipolar and 0.5-1.0 ppm for the chemical shift dimension. vR = 1.07 kHz. (b) Dipolar cross-sections taken from the 2D spectrum. Each trace runs parallel to ivh through a particular rotational sideband in u>2. (i) Experimental i5N-H spectra from [15N]acetylvaline, vR = 1.07 kHz. The two simulations (ii and iii) assume two different orientations of the dipolar and shielding tensors, (ftD = 22°, D = 0°) and (Ai = 17°, aD = 0°), respectively, and illustrate the subtle differences in orientation which can be detected in the spectra. 

Some early attempts were made to determine anisotropies from second-moment analysis in which use is made of the anisotropic contribution to the observed second moment.5 6 Limitations of this method are the need for large shifts and fields and the often-required assumption of axial symmetry of the shielding tensor. In 1968 a method was reported that uses coherent averaging techniques7 to effectively narrow the dipolar-broadened lines of powdered solids. The observed spectrum is curve-fitted using a computer-broadened theoretical chemical shift distribution to give the principal components of the shielding tensor. 

The dependence of the Si -spin dynamics on the S2 chemical shielding tensor will in general increase the number of spin parameters, which have to be known or determined for a meaningful evaluation of the experimental results. This is certainly a disadvantage when the only goal is extraction of dipolar coupling information. But even for cases where it is feasible to extract all dipolar and... 

---