Spectral Density Functions for Diffusion Through Disordered Materials

Abstract

The purpose of this thesis is to examine the nuclear spin relaxation results for diffusion in a disordered system. This is complicated as the presence of the disorder means that the spins no longer diffuse about the system in a simple, regular manner. The way in which the disorder is manifest in the system is difficult to know exactly and the modelling can be difficult and time consuming for a large system with many spins present. For this thesis it was decided to examine the relaxation rates by modelling the diffusion exactly for a small, finite system at a low concentration of spins. The time constants T₁and T₁p can then be calculated exactly and compared to both experimental and theoretical work carried out on much larger systems. The purpose of this was to see how accurately a small system could model the real, large scale systems and to gain some insight into the mechanisms behind the diffusion process in a disordered system.