Spin-lattice relaxation in¹³CH₃compounds: application to¹³C enriched aspirin

Abstract

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 ωt, + ωC = ωH, 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.