Weak-Diffusion Theory of NMR Signal in Magnetically Heterogeneous Media

A general theory is developed for the effect of molecular diffusion on the NMR signal obtained from magnetically heterogeneous media in the limit of weak diffusion. The theory is based on a rigorous expansion in the diffusion constantD, with the correction to first order inDbeing given explicitly for unrestricted, isotropic diffusion. The expansion allows for an arbitrary sequence of field gradients and 180° spin-flip pulses, making it applicable to a wide variety of NMR protocols. The theory may be useful for estimating the magnitude of diffusion effects and in determining some of a medium's microscopic magnetic properties.