The carbon-13 spin-lattice relaxation times were measured by use of the inversion-recovery pulse sequence [180°-t-90°] for the methyl and carboxylate carbons of 1-, 2-, and 1,2-13C-labeled sodium acetates in deuterium oxide at several temperatures. The relaxation of the two carboxylate carbons was found to follow single-exponential behavior with different recovery rates. The more rapid carboxylate-13C relaxation in the doubly labeled species was attributed to the simple additional 13C-13C dipolar interaction, on the basis of which the effective correlation time for the rotation about the C-C axis, τeff(CC), was calculated. In the case of the methyl group, the pure 13C-1H dipolar relaxation rate was determined with a combination of the observated relaxation rate and the proton nuclear Overhauser enhancement factor for the methyl carbon, and the effective correlation time for the rotation about the C-H axis, τeff(CH), was evaluated. The overall and methyl internal rotational diffusion constants, D and Dint, were deduced from the values of τeff(CC) and τeff(CH) on the basis of the stochastic diffusion model. The temperature dependence of D and Dint was found to follow Arrhenius-type behavior with mean activation energies of 24 and 9.8 kJ mol-1, respectively. The latter one can be related to the threefold V3 barrier for the methyl internal rotation, and finally the torsional vibrational frequency for the methyl group was estimated to be 204 cm-1.
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