Limiting behavior of 2H spin lattice relaxation in molecules with multiple internal rotations

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Abstract
Expressions for the dependence of deuteron relaxation times for CD bond vectors on the number of internal rotations, N + 1, in polymeric chains and side chains of micelles and phospholipid vesicles have been derived for large N. The expressions are valid for molecules in which : (i) the diffusion tensors have ellipsoidal symmetry,(ii) all angles between successive pairs of internal rotation axes are equal, and (iii) the internal rotations are independent and all diffusion coefficients for internal rotation are equal. For molecular entities with spherically symmetric rotational diffusion tensors, the asymptotic relation simplifies to the following relation: where DO is the rotation diffusion coefficient, D the diffusion coefficient for internal rotation, ω0 is the magnetic resonance frequency, and QD is the quadropole coupling constant for the CD bond vector. For hydrocarbon chains the relaxation rate is within 10% of its asymptotic value for relatively small N (about 6) and converges rapidly to the asymptotic relaxation rate as N is increased.

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