Effects of disorder in polymer morphology on spin diffusion

A diffusion equation appropriate to the nuclear magnetic resonance spin diffusion experiments is analyzed using a periodic lattice model. In this model, the initial magnetization resides only in domains of one of the phases in a multiphase system. These domains are arranged according to a lattice with well-defined lattice spacing. Disorders are incorporated by introducing variations in the domain sizes, in orientations of the domains with respect to primitive basis vectors of the lattice, and in the occupancy of the lattice site. By means of a spatial Fourier analysis, it is shown that because of spin diffusion, the initial magnetization decays within a time scale of (B/2 pi)(2)/D when there is no disorder. B is the lattice spacing, and D is the spin diffusion coefficient. When there are disorders due to vacancies at the lattice sites or variations in the domain sizes, the magnetization decays much slower and follows a power law at long time. The slower decay is due to the introduction of the long wavelength modes by the disorders. The orientation disorder, however, does not lead to a slower decay, and the zero wavevector mode is forbidden.