Powder lineshape

Fig. 2 Mechanically oriented bilayer samples as a membrane model for ssNMR. (a) Illustration of the hydrated lipid bilayers with MAPs embedded, the glass supports, and the insulating wrapping, (b) A real sample consists of 15 stacked glass slides, (c) Schematic solid-state 19F-NMR lineshapes from an oriented CF3-labelled peptide (red), and the corresponding powder lineshape from a non-oriented sample (grey), (d) Illustration of typical orientational defects in real samples - the sources of powder contribution in the spectra...

Another way of dealing with the resolution problem for powder lineshapes is to use multidimensional NMR techniques to separate powder pattern lineshapes (or magic-angle spinning sideband patterns) according to isotropic chemical shift, as mentioned previously. 

For this reason, the study in question19 examined a sample of high-density polyethylene that was iso topically labelled with, 3C so as to produce isolated 13C spin pairs. Static 13C powder lineshapes were then observed as a function of temperature. Analysis of these by lineshape simulation shows that, indeed, the polyethylene chains do undergo 180° chain flips. The static lineshapes in this case result from the sum of chemical shift anisotropy and dipolar coupling. However, the chemical shift anisotropy is known and, as mentioned previously,... 

The effect of chemical shift anisotropy on 2H powder lineshapes has also been discussed.35 Another study emphasizes the importance of recording 2H... 

Since the intrinsic lineshape has finite width, the experimentally observed lineshape is the convolution of 1(f) with one of the lineshape functions g(f). A powder lineshape for an axially symmetric chemical shielding tensor is shown in Fig. 4 and a typical example of a general powder lineshape is shown in Fig. 5. Many systems yield lineshapes close to that of a powder pattern and the mathematical properties of these lineshapes are discussed in detail by Alexander et al.iA... 

Fig. 4. A powder lineshape for an axially symmetric tensor shown as a function of frequency. The frequency scale is given in units of Af, hence the intensity scale is in units of 1 / Af The frequency is shown increasing to the left, since it is conventional to display NMR spectra as if they were measured under CW conditions with the frequency held constant and the magnetic induction shown increasing to the right.

Figure 15.17 shows 2H spectra of powdered hexamethyl-benzene-D g. Since we are dealing with a powder, we expect powder patterns, and the back-to-back superimposition of a pair of asymmetric powder lineshapes is clearly seen. Quad-rupolar interactions can get quite large, and in most cases they will dominate the chemical shift spectrum. For deuterium, which has a rather tiny quadrupole moment, the quadrupolar interaction varies from about 25 kHz in hexamethylbenzene-D g to about 200 kHz in carboxylate deuterons. In the heavier nuclei, such as 127I, the quadrupolar interaction can reach 2000 MHz No one is ever likely to observe a spectrum that wide. 

Figure 2.15. Effect of a distribution of interactions on the second-order quadrupole powder lineshape of the central transition in detail with the mean interaction Xq = 2 MHz and -ri = 0 at a Larmor frequency of 80 MHz showing A. no distribution, B. a Gaussian distribution of isotropic chemical shifts with FWHM = 0.17 A, C. a Gaussian distribution of the quadrupole interaction of 340A and D. both the chemical shift and quadrupole interactions distributed, (A = 2344Hz).

This term is anisotropic and produces a powder pattern. It has been derived under the assumptions that first-order perturbation of the S-states is sufficient, that the J tensor is axially symmetric and that the unique axis of J is aligned with the intemuclear vector. Under MAS this term will be scaled but, as it is not proportional to P2(cos0), it cannot be completely removed. Hence the MAS spectrum will still have some residual width, but the most profound effect is to leave an isotropic term which can be calculated by averaging the powder lineshape. Hence for a J-coupled system with an axially symmetric quadrupole interaction, the spectrum is shifted from the isotropic chemical shift by ... 

Figure 8.36. A selection of Mo NMR spectra of molybdenum compounds. A. Observed MAS spectrum of M0O3 (lower) with simulation (upper). B. Powder lineshapes of the central transition of MoSct (upper) and M0S2 (lower). C. Observed powder lineshape of the central transition of M02C (lower) with the simulation (upper). From Bastow (1998), by permission...

Cross polarisation from H to Mo has been shown to produce enhancements of 66-86% of the theoretical maximum and reliable second-order powder lineshapes in isotopically-enriched compounds such as (NH4)6Moy024.4H20 and (Bu4N)2Mo207 which contain suitable proton sources (Edwards and Ellis 1990). The optimum contact times were found to be 20-30 ms and the value of Tip for molybdenum is long by comparison with the other relaxation processes, making this a suitable candidate for CP. 

Figure 11.3. A. Zn NMR room-temperature powder lineshape of zinc metal showing the central transition (upper) and the ( /2) satellite transitions (lower). From Bastow (1996) by...

Figure 11.8. A. Width of the NMR resonance of various cubic Nii Alx alloys as a function of temperature. Note that only the highest-Ni alloy Nio.46 AI0.54 shows a significant change in linewidth with temperature. B. Temperature dependence of the Al powder lineshape of Ni2Ala. Note the evolution of the 2 room-temperature overlapping quadmpole lineshapes into a single line as the aluminium atoms jump between the 2 sites with increasing temperature.

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