Superpositions of intramolecular reorientations and nuclear spin relaxation

Abstract

A general expression is developed for the dipole-dipole nuclear spin-lattice relaxation time T ₁ in molecules whose constituents are undergoing an arbitrary number (n) of superimposed reorientations about different molecular symmetry axes. In addition, the calculation takes into account isotropic tumbling of the whole molecule for the case of a liquid, or, a powder average for the case of a powder or polycrystalline sample. As an example, the case of n = 3 (three superimposed reorientations plus tumbling or a powder average) is investigated. The incentive for treating the n = 3 case is the need to interpret relaxation measurements (reported in the accompanying paper) in 4,4′-methylenebis (2,6-di-t-butylphenol) where, in addition to methyl and t-butyl reorientation, the benzene rings may be reorienting with respect to one another. The calculation draws upon the general theory of spin-lattice relaxation and on existing calculations concerned with the effects that superimposed reorientations have on correlation functions. The resulting expression for T ₁ is much more general than previous calculations which have only been done for n = 2 and even then only for specific geometries. It is shown that the present expression for T ₁ reduces to those determined previously in the appropriate special cases.