Spin-echoes for diffusion in bounded, heterogeneous media: A numerical study

The diffusive behavior of spin-bearing species in a bounded heterogeneous medium is analyzed in a manner appropriate for spin echo experiments in the presence of field gradients. A numerical method based upon the stochastic Liouville equation (SLE) is discussed that includes the discontinuities in transport and solubility properties due to the different spatial regions. The double step computational algorithm, which takes advantage of the different time scales of diffusive and spin-quantum phenomena, is then introduced as a general approximate solution of the time dependent SLE. This method is applied to the calculation of the decay of spin echo amplitudes, and it suggests a new approach for analyzing such experiments in terms of the microscopic details and chemical properties of heterogeneous systems.