Two-dimensional nuclear magnetic resonance with sample flip for characterizing orientation distributions, and its analogy to x-ray scattering

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Abstract
A two‐dimensional (2D) exchange NMR (nuclear magnetic resonance) experiment with sample flip during the mixing time (direction exchange with correlation for orientation‐distribution evaluation and reconstruction, DECODER) is presented, which allows investigation of molecular order in great detail. For anisotropic NMR interactions with axial symmetry (η=0), the features of the orientation distribution of certain molecular axes are reflected directly in the distribution of the intensity in the 2D spectrum. The orientation distribution in terms of two angles can be largely reconstructed by a simple rearrangement of the spectral intensity. Analogies between this NMR experiment and wide‐angle x‐ray scattering (WAXS) techniques for pole figure analysis are identified. Practical aspects of the DECODER method are considered in detail, e.g., sample orientations that are particularly suited for elucidating biaxiality with high resolution, or that are convenient in terms of sample preparation. Even with spectral overlap and for η≠0, the degree of order can be read immediately from the spectrum. Simulations and experimental 2H NMR spectra for deuterated polyethylene serve to exemplify the method.