Quadrupolar lineshape analysis

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],... 

Motions with rates of the order of the nuclear spin interaction anisotropy can be assessed via lineshape analysis. These are generally motions of intermediate rates, a few kHz to tens of kHz for chemical shift and dipolar interactions, higher for quadrupolar interactions. 

In view of the dominant quadrupolar interaction of deuterium, its weak dipolar and chemical shift interactions can be neglected, which simplifies the theoretical analysis of the quadrupolar lineshapes and relaxation data (see Sections 6.2.2 and 6.2.3). 

Lineshape analysis of or NMR signals arising from the quadrupolar interaction or chemical shifts anisotropy, respectively, can yield invaluable information about amplitude and motions in the solid [3,150-156]. The quadrupolar interaction, in particular, dominates the spectral pattern in NMR. The frequency of a deuterium resonance in the absence of molecular motion is given by... 

Analysis of dipolar or quadrupolar relaxation restricts the dynamic range of rate constants to those on the order of the fre-quency of the Bq field (yBq Slower rates (10 < k < lo ), comparable to those available from lineshape analysis, can sometimes be obtained by analysis of relaxation in the rotating frame (Tj p). Application of a 90° pulse followed by a continuously applied 90° phase-shifted pulse maintains the magnetization vector in the xy plane. The rate of loss of magnetization in the xy... 

If there is some molecular motion with characteristic times on the order of ICT sec, the NMR spectrum will no longer have the Pake doublet lineshape discussed earlier. For example, in gel-phase bilayers a perdeuterated lipid acyl chain will have a broad, relatively featureless spectmm, as shown in Fig. 3. These spectra do not lend themselves to easy analysis The molecular motion in the membrane is not rapid enough to be axially symmetric (see the description of the fluid bilayer below) on the NMR time scale but is fast enough to influence the average value of the quadrupolar interaction and thus the splittings of the individual labels. 

Summation of slices parallel to F2 of individual 2D peaks (primarily in crystalline materials) provides the complete assignment of x and rj by either simulating the extracted lineshapes or by other means such as moment analysis " and direct observation. Data from amorphous materials are harder to interpret since the projection of their 2D peaks on to the F2 dimension exhibits distributions rather than well-defined second-order quadrupolar MAS lineshapes. Yet, they can be analysed by spectral inversion, full 2D simulations or direct observation, as will be shown at the end of this section. 

The use of NMR spectroscopy for probing molecules adsorbed on alumina dispersions is briefly cited. Soderlind and Blum [66] used deuterium NMR to probe the dynamics and structure of a surfactant (an alkylbenzenesulfonate, SHBS) adsorbed onto alumina. The phenyl ring was deuterium-labeled, and from the analysis of the lineshapes of H spectra, valuable information on the degree of motional freedom in the adsorbed layer was obtained. As deuterium possesses a quadrupole moment, it is sensitive to the orientation of the molecule with respect to the external magnetic field. This sensitivity generates a quadrupolar splitting, which is defined as the separation between the two allowed transitions for the deuterium nucleus. In liquid systems, the quadrupole interaction is averaged out, but for static systems powder... 

For nuclei such as H with a spin of unity the strong quadrupolar interaction ( 100 kHz) dominates over the dipolar and chemical shift interactions and helps to simplify the analysis of the lineshapes. Selective deuterium labeling of ligands and/or proteins therefore offers considerable potential, not only for molecular distance information but also for studying the dynamics of the interactions. 

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