Spin relaxation based nuclear magnetic resonance (NMR) methods have been used extensively to determine pore size distributions in a variety of materials. This approach is based on the assumption that each pore is in the fast diffusion limit but that diffusion between pores can be neglected. However, in complex materials these assumptions may be violated and the relaxation time distribution is not easily interpreted. We present a 2D NMR technique and an associated data analysis that allow us to work directly with the time dependent experimental data without Laplace inversion to identify the signature of diffusive coupling between different pores. Measurements on microporous glass beads and numerical simulations are used to illustrate the technique.

We present numerical simulations of a two-dimensional (2D) nuclear magnetic resonance process, T_{2}-storage-T_{2}, on a simple mixed porosity system, the micrograin consolidation (μGC) model. The results of these calculations are compared with predictions based on the analytic two-site exchange model, for which we have independently established numerical values for all the input parameters. Although there is qualitative and semiquantitative agreement between the two models, we identify specific instances where the two-site model fails to properly describe the combined effects of relaxation and diffusion. Generally, these instances occur when a gradient in magnetization within the large pores of the μGC model is established during the initial phase of the 2D process. The two-site model assumes that the magnetization is spatially uniform within each of its subpore systems and thus cannot describe such effects.