Spin-lattice relaxation in 13CH3 compounds: application to 13C enriched aspirin

Spin-lattice relaxation processes in ¹³CH₃ groups in methyl compounds are studied both theoretically and experimentally. The four spin-½ nuclei in such methyl groups give rise to 16 spin-rotational states, which are split by rotational tunnelling. From the corresponding populations (15 independent) five long lived combinations are formed: the ¹³C magnetization M _C, proton magnetization M _H, tunnelling energy TE, rotational polarization RP and dipolar energy DE. Their spin-lattice relaxation via the transitions induced by the ¹³C-proton dipolar interaction is studied in detail. Direct relaxation rates and coupling terms between these combinations are derived. Predictions are compared with experimental data for ¹³C spin-lattice relaxation at 75.4 MHz in 99% enriched (only methyl carbons enriched) single crystal of aspirin. Above 40 K, the M _C recovery is exponential and describable in terms of the direct relaxation transitions without couplings. The same is true for the initial relaxation in the region of non-exponential relaxation between 30 K and 40 K. The orientation dependence of the initial relaxation rate agrees with the theoretical calculations. The non-exponentiality is related to resonant level-crossing transitions with ω_t, + ω_C = ω_H, where the angular frequencies represent rotational tunnelling and carbon and proton resonances, respectively. The resonant transitions produce couplings between M _C, M _H and TE that are described quite accurately by the present model.