NMR magnetic dipolar spectral density functions for two-dimensional lattice diffusion

Abstract

NMR magnetic dipolar spectral density functions are obtained for some lattice diffusion models for two-dimensional lattice diffusion and compared with the results for the BPP and continuum models. The systems considered are dipolar interactions between spins diffusing in a plane, and interactions between diffusing spins in a plane with fixed spins in a separate parallel plane. Numerical results and analytic approximations are obtained for spins diffusing on square lattices. The BPP model is unsatisfactory in both magnitude and functional form in two-dimensional systems. The continuum and lattice diffusion models agree for interactions between well separated planes, but there are significant differences between the continuum and lattice models otherwise. Results for the longitudinal spin relaxation rates in the laboratory and rotating frames are obtained for square lattices, and show a strong dependence on the direction of the applied magnetic field relative to the crystal axes.