Powder patterns lineshape analysis

The difference between the Markov model lineshapes and those from the Smoluchowski model is particularly pronounced when the diffusion coefficient is of the order of the quadrupole coupling constant. In the limit of large diffusion coefficients, the two models converge, and in the limit of low diffusion coefficients, the spectra are dominated by small-amplitude oscillations within potential wells, which can be approximately modelled by a suitable Markov model. This work strongly suggests that there could well be cases where analysis of powder pattern lineshapes with a Markov model leads to a fit between experimental and simulated spectra but where the fit model does not necessarily describe the true dynamics in the system. 

Another study used the VACSY experiment discussed in Section 2.2 to examine the molecular motion in the crystalline region on poly(e-caprolactone) via lineshape analysis of l3C chemical shift anisotropy powder patterns.79... 

Chemical shift relative to liquid CS2, some are peak positions not the isotropic shifts, see original references. Numbers in parentheses represent singularity positions of MAS powder patterns, t Estimated upper limit of the quadrupole effect parameter, except which is based on lineshape analysis. 

One-dimensional quadrupole echo NMR lineshape analysis of powder samples is particularly informative when fast, discrete jumps occur between sites of well-defined geometry as, for example, in a phenyl group undergoing two-site exchange. In this case, the characteristic Pake-pattern is transformed into an axially asymmetric lineshape with an apparent asymmetry parameter r] 9 0 (see Equation (6.2.3)) [1-8]. The asymmetric lineshapes, shown on the left in Fig. 6.2.2, can be derived by considering how the individual components of the principal EFG tensor become averaged by the discrete jumps. Within the molecular frame, and in units of as defined by Equation (6.2.2), the static axially symmetric tensor consists of the components = 1, = — 1/2, and V y = — 112. This traceless tensor satisfies the... 

If powder spectra of the type shown in Fig. 9.3 and 9.4 can be obtained experimentally, the principal values of the anisotropic interaction in question (though not the orientation of the PAS with respect to a fixed frame) can be obtained by a straightforward lineshape analysis. However, to obtain such spectra, it is necessary that there is only one distinct nucleus, and that one anisotropic interaction dominates. Usually, the static NMR lineshape is a broad featureless hump due to the overlapping of many powder patterns as well as the interplay of the different broadening mechanisms. As an example of this. Fig. 9.5 presents a NMR spectrum of a representative organic sohd, together with, for comparison, the corresponding solution-state spectrum. It is to be noted that the problem in such a case is not a lack of information, but rather there is essentially an overload, such that the net effect is the virtual loss of all information. In the remainder of this article, soHd-state NMR approaches by which this information can be recovered wiU be demonstrated. 

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