Proton spin diffusion in polyethylene as a function of magic-angle spinning rate. A phenomenological approach

Starting from the phenomenological Bloembergen-Purcell-Pound equation a relation between magic-angle spinning (MAS) rate and spin diffusion is derived. The resulting model equation was fitted to observed spin diffusion versus MAS rate data obtained at 298 K on an high-density polyethylene sample, revealing a reduction in the effective spin diffusivity by (65 + 5)% when increasing the MAS rate from 2 to 12 kHz. The same model equation enabled the rigid-lattice diffusivity to be estimated and was found to be only slightly higher, by approximately 10%, compared to the spin diffusivity observed at the lowest MAS rate applied (2 kHz). Moreover, the model equation predicts a reduction in the effective spin diffusivity by more than 90% when increasing the MAS rate to more than 30 kHz.