13C NMR rotating frame relaxation in a solid with strongly coupled protons: Polyethylene

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Abstract
The validity of interpreting measured rotating frame relaxation times, T1ρC*, in terms of molecular motion is investigated for crystalline, oriented, linear polyethylene (PE) as a representative rigid organic solid with reasonably strong dipolar couplings. T1ρC* data are presented at three temperatures, −100, 28, and 100 °C and for 13C rf fields, ν1C, in the range 35<ν1C<90 kHz, for the orientation where B0 is parallel to the PE chain axes. With the exception of the T1ρC* data taken at ν1C≳80 kHz and T=100 °C, all T1ρC* data observed were determined not by molecular motion, but rather by spin–spin effects in which the spin-locked carbon system seeks to equilibrate with the proton dipolar system with a characteristic time constant TCHD(ν1C), while at the same time the proton dipolar system is equilibrating with the lattice with a time constant T1D. The TCHD values deduced from T1ρC* support existing theory which predicts that TCHD(ν1C) ∝ exp(2πν1CτD) where τD is the correlation time for dipolar fluctuations. A calculation of τD from PE crystal structure agrees very well with the experimentally determined τD of 24 μs. Further experimental proof of the importance of the spin–spin contribution to T1ρC* is demonstrated via changes in the carbon rotating frame magnetization, MSL(τ), for differing states of proton dipolar order. The question of extracting information about molecular motion from T1ρC* data is examined under the assumption that the total reduced correlation function for the local proton dipolar field at a carbon nucleus is the product of a Lorentzian reduced correlation function describing dipolar fluctuations and an exponential reduced correlation function describing molecular motion. It is shown for molecular motion in the long correlation time regime and for sufficiently large ν1C that contributions to T1ρC* from molecular motion and dipolar fluctuations are cleanly separated. Pertinent background material for the interpretation of T1ρC* data is also presented; this includes effects of sample spinning, transients in carbon and proton magnetization, and ambiguities which arise when molecular motion is fast enough to cause some averaging of the static dipolar line shape. Criteria are offered whereby one can decide on the validity of interpreting T1ρC* data in terms of molecular motion. As an example, the T1ρC* data point for ν1C=87 kHz and T=100 °C is interpreted in terms of molecular motion and the deduced correlation time, assuming a flip–flop motion of the polymer chains, is shown to be qualitatively consistent with published proton T1ρH results. Finally, 13C longitudinal relaxation time measurements are discussed as a possible alternative to T1ρC* for obtaining information about molecular motion.