Scaled chemical shift anisotropy

Multiple pulse sequences average the dipolar Hamiltonian, but also affect other Hamiltonians to an extent which depends on the particular sequence. For example, the WAHUHA sequence scales chemical shift anisotropies by a factor of l/VS. 

Several methods have been developed to determine the chemical shift anisotropies in the presence of small and large quadrupolar broadenings, including lineshape analysis of CT or CT plus ST spectra measured under static, MAS, or high-resolution conditions [206-210]. These methods allow for determination of the quadrupolar parameters (Cq, i)q) and chemical shift parameters (dcs, //cs> <5CT), as well as the relative orientation of the quadrupolar and chemical shift tensors. In this context, the MQMAS experiment can be useful, as it scales the CSA by a factor of p in the isotropic dimension, allowing for determination of chemical shift parameters from the spinning sideband manifold [211],... 

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

The second term leads to a vestigal powder pattern, scaled down by J2e. The rule of thumb becomes to reduce chemical shift anisotropy by a factor of 100, set the angle to within about 1/2 degree. 

In general, multiple pulse techniques sufficiently average the dipolar interactions, compress the chemical shift scale, but they do not affect heteronuclear dipolar interactions and the chemical shift anisotropy. A combination of both multiple pulse techniques and magic angle spinning, so-called CRAMPS (Combined Rotational And Multiple Pulse Spectroscopy) is found to yield satisfactory results in the solid state H NMR of solids 186). The limitations of all these techniques, from the analytical point of view, arises from the relatively small chemical shift range (about 10 ppm) as compared with some other frequently studied nuclei. However, high resolution H NMR of solids is useful in studies of molecular dynamics. 

Characterization of the polymer primary structure is best carried out using solution NMR methods due to the increased spectral specificity of solution NMR methods as compared to solid state NMR methods. Solution NMR methods here includes solutions, gels, dispersions, melts, etc. Any method involving dilution, dispersion, increased temperature, etc. that will introduce sufficient motion into the polymer chain such that the unwanted nuclear spin interactions can be averaged to their trace values (zero for dipolar, isotropic chemical shift for the chemical shift anisotropy, scalar coupling for the indirect dipolar interaction, and zero for quadrupolar), on a sufficiently short time scale. 

This technique is based on the large chemical shift anisotropy exhibited by lipid phosphorus. In the presence of proton decoupling, this anisotropy results in characteristically broad spectra whose shape and width depend on phospholipid motion in turn, this is related to the lipid phase. In large bilayer structures (radius greater than 200 nm), as is the case for most biomembrane preparations, the only possibility of motion at the NMR time scale (10 s) is the rotation of the phospholipid molecules about their long axis. The result is a very broad spectrum with a low-field... 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

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