Abstract
Chemical shift tensors in C solid-state NMR provide valuable localized information on the chemical bonding environment in organic matter, and deviations from isotropic static-limit powder line shapes sensitively encode dynamic-averaging or orientation effects. Studies in C natural abundance require magic-angle spinning (MAS), where the analysis must thus focus on spinning sidebands. We propose an alternative fitting procedure for spinning sidebands based upon a polynomial expansion that is more efficient than the common numerical solution of the powder average. The approach plays out its advantages in the determination of CST (chemical-shift tensor) principal values from spinning-sideband intensities and order parameters in non-isotropic samples, which is here illustrated with the example of stretched glassy polycarbonate.
Highlights
Chemical-shift anisotropy (CSA) is one of the most useful interactions in solid-state NMR, as the principal values of its tensor span a convenient frequency range for many relevant heteronuclei present in organic materials, such as 13C, 15N or 31P
The most complete information would be the extraction of the full orientation distribution function (ODF), which is best achieved with the dedicated DECODER 2D experiment involving a mechanical sample flip (Schmidt-Rohr et al, 1992) or with some compromises in special cases even from 1D spectra (Hempel and Schneider, 1982)
The anisotropy can be quantified by orientational moments, which are proportional to expansion coefficients of the orientation distribution in terms of Legendre polynomials
Summary
Chemical-shift anisotropy (CSA) is one of the most useful interactions in solid-state NMR, as the principal values of its tensor span a convenient frequency range for many relevant heteronuclei present in organic materials, such as 13C, 15N or 31P. Excluding effects of intermediate motions on the NMR timescale, deviations from the static-limit isotropic powder line shapes, characterized by the three principal values or the three commonly derived invariants (isotropic shift, anisotropy and asymmetry), are immediately informative about the geometry of fast-limit motions (Kulik et al, 1994; Titman et al, 1994) as well as orientation effects in non-isotropic samples (Maricq and Waugh, 1979; Hentschel et al, 1978). The latter are the main concern of this contribution. One key advantage of our approach is its flexibility to change the CSA principal values and the related angles at no additional expense in calculation efficiency
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