Ambient-temperature13C linewidth (LW) and transverse relaxation (TC2) data are presented for the natural-abundance crystalline carbons of linear polyethylene (LPE) under CW proton decoupling conditions and magic angle spinning (MAS). This linewidth behavior typifies that seen for rigid methylene carbons whose attached protons are also strongly coupled to other protons. These data are presented for two LPE samples (unoriented, melt-crystallized and uniaxially oriented, extruded) as a function of several parameters including static field (1.4 T <B0< 9.4 T), proton decoupling field strength (38 kHz < νH1< 90 kHz), MAS frequency (0.5 kHz < νr< 8 kHz) and RF frequency offsets from resonance (−4 kHz < Δνoff< 4 kHz). It is the ubiquitous nature of off-resonance proton irradiation (ORPI) (arising from fixed or rotationally dependent deviations from the true proton resonance condition) which provides the focus for this work. Corresponding contributions, LW(ORPI), to the total LW are treated within the general framework of the effective-field picture of CW decoupling. Then, considering the presence of spin fluctuations characteristic of the strongly-dipolar-coupled protons of LPE, LW(ORPI) can be traced to orbit-dependentTC2contributions to LW. Important dependences demonstrated and discussed include: (1) For “off-resonance” decoupling, there is a quadratic dependence of LW(ORPI) on (Δνoff/νH1)andthere is a strong dependence of the corresponding parabolic coefficient on νr. From the latter dependence, characteristic times for spin fluctuations are also estimated. (2) For “on-resonance” decoupling, LW(ORPI) is proportional to (νH1)−2andshows very little sensitivity to νr. These LW(ORPI) contributions become more important at higherB0since the principle reason for ORPI is the chemical shift anisotropy (CSA) of the13C-bonded protons. The difference in sensitivities of LW(ORPI) to νrfor the off-resonance and the on-resonance cases is traced back, respectively, to the scalar property of Δνofffor RF frequency offsets and to the tensorial character of the proton CSA. Contributions from LW(ORPI), possibly much larger than those seen in LPE, can be expected when protons near13C nuclei sense any non-scalar, rotor-position-dependent magnetic fields, e.g., (a) local dipolar fields associated with third, magnetic nuclei or (b) perturbing magnetic-susceptibility fields arising from paramagnetic or ferromagnetic inclusions in a sample. By understanding the contributions to LW in LPE, one can forecast much more precisely what the potential benefits will be from new decoupling schemes like the recently reported “two-pulse phase modulation” (TPPM) since TPPM is designed to reduce LW(ORPI). Aside from LW(ORPI) contributions, the experimental LW data cover parameter space where another broadening mechanism, namely, MAS-assisted dipolar fluctuations (MADF), is seen. This mechanism, also recognized by others, creates aTC2-type linewidth contribution which increases rapidly as νH1decreases and which additionally has some orbit dependence. If the current trend in13CCPMAS is toward higherB0and νr, the νr-dependent MADF contributions can easily dominate LW relative to theB0-dependent LW(ORPI) contributions. One can avoid serious MADF broadening; however, the minimum acceptable values of νH1for good decoupling rise rapidly withB0. Finally, a few LW measurements are made on methyl-α-d-glucopyranoside tetraacetate (MGT), a rigid, polycrystalline material containing carbons with 0, 1, 2, and 3 attached protons. The behaviors of the methylene, methine, and methyl carbons at 9.4 T are compared with the behavior of LPE.
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