Modeling the impact of decay due to diffusion in internal gradients on NMR data

In porous materials, the NMR decay rate includes contributions from three different relaxation mechanisms: bulk fluid relaxation, surface relaxation, and decay due to diffusion in the internal magnetic field (DDIF). The contribution to the total decay rate from DDIF will depend on the experimental parameters, the length scale of the pores, and the magnitude of internal field gradients. Commonly, interpretation of NMR data assumes that the contribution of DDIF is negligible. To test this assumption, we used existing theory to model decay due to diffusion over a range of parameter values and to generate synthetic NMR data. We considered the three asymptotic diffusion regimes: free diffusion, motional averaging, and localized dephasing; as well as intermediate behavior where diffusion occurs in multiple regimes. Inversion of the synthetic data was performed, and the impact of DDIF on the 1D relaxation time distribution and 2D relaxation time - diffusion distributions was assessed. This work shows that, under certain conditions, DDIF will significantly impact the calculated distributions of NMR relaxation times and diffusion coefficients. This impact can be reduced by selecting appropriate measurement parameters or by accounting for DDIF in the inversion using an appropriate estimate of the internal gradient magnitude. The example artifacts observed in the results from the synthetic data can be used to recognize artifacts from DDIF in data and aid in interpretation.