Efficient polynomial analysis of magic-angle spinning sidebands and application to order parameter determination in anisotropic samples.

Chemical shift tensors in ${}^{13}$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 ${}^{13}$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.