a Theoretical Study of Molecular Reorientation and Nuclear Spin-Lattice Relaxation in Solids

The dependence of the solid-state proton spin -lattice relaxation rate R on reorientational motion is studied theoretically. The geometric dependence of the expressions for R allows the relative positions of the protons to be specified arbitrarily; the restriction that the two protons remain a fixed distance from each other as they move, inherent in most previous analyses, has been removed. This allows more realistic cases to be considered; the lengths of the vectors between protons may change during the reorientation process, and the directions of these vectors need not change isotropically. A general hopping model for the motion of spins among a set of discrete positions is developed. Three specific models of motion are presented, one which assume the motion of the protons to be a continuous diffusion process and two which assume that the protons hop among several discrete locations. The spin-lattice relaxation rate R is derived for each of these models. The specific form of R is found for several simple geometries; these expressions are used to obtain the relaxation rate for two protons in a variety of organic molecules. Relaxation rates for entire molecules are calculated from these results, and in some cases compared with previous analyses. This dissertation is organized so that the analysis proceeds from general to specific. Much of the general theory is new, as are many of the results specific to proton -proton interactions and entire molecules. Points of interest which have not been thoroughly investigated are so noted, in order to serve as seeds for future research. Heavy use was made of Mathematica^{circler }.