DIPOLE-DIPOLE SPIN RELAXATION IN SOLIDS - THE UNRESTRICTED HOPPING MODEL AND THE METHYL PROTON NON-METHYL PROTON INTERACTION

We develop a stochastic model for molecular reorientation which leads to the calculation of the dipole-dipole spin-lattice relaxation rate in cases where the length of the spin-spin vector changes with time. The calculations are applied to methyl group rotation-induced relaxation in planar methyl-substituted aromatic molecules like methylnaphthalenes, methylanthracenes and methylphenanthrenes. Our theory considers an unrestricted hopping model in which the spin-spin vector hops from one position to any of its other allowed positions. A general discussion of the relaxation process is presented and a variety of general geometries for the motion of pairs of spins is considered. The case of a reorienting methyl group is considered in some detail. The relaxation rate resulting from the interaction between methyl protons and any other fixed proton is then presented. The general approach is appropriate for a large class of molecular solids. We compare previously determined experimental relaxation rates with the current theory for methyl-substituted naphthalenes, anthracenes and phenanthrenes. We show that the geometry for peri-substituted methyl groups corresponds to the situation where the two methyl protons near the peri hydrogen lie out of the plane of the aromatic ring. This expected result is in agreement with laser jet spectroscopy experiments and ab initio calculations for 1-methylnaphthalene.