13C Magnetic Relaxation in Micellar Solutions. Influence of Aggregate Motion on T1

The 13C T1 NMR relaxation times of the carbon atoms in the alkyl chains of a micelle-forming amphiphile are discussed. A theoretical model for the relaxation process is developed. The relaxation in a 13C1H2 methylene group is treated in detail using a density matrix formalism. In modeling the molecular dynamics of the system the emphasis is placed on a separation between a fast local motion within the micelles and a slower overall motion associated with the aggregate itself. In applying the model to octanoate micelles it is shown that, using previously determined structural parameters, it is possible to obtain an a priori estimate of the contribution from the slow motion to T1 of the individual carbons. Particularly for the carbons close to the polar group, the overall motion giyes a substantial, and probably dominating, contribution to T1. It also emerges that the T1's should be frequency dependent. The predictions of the model are tested against experimentally determined T1 values for four carbons in sodium octanoate micelles and a surprisingly good agreement is found. Particularly the observed frequency dependence of T1 shows unequivocally that the slow micellar motion contributes to the spin-lattice relaxation. It also follows that the alkyl chain motion within the micelles is very rapid. The interior of the micelle is thus even more liquid-like than has been inferred previously from 13C T1 measurements. © 1979, American Chemical Society. All rights reserved.