Influence of weak molecular velocity autocorrelation on the diffusion NMR

Abstract

Self-diffusion of spin-bearing molecules measured by magnetic resonance can noninvasively probe the microstructure of complex soft matter and serve as a powerful tool for different types of diagnostics. Theoretical methods are needed to determine the autocorrelation of molecular velocities and magnetic resonance signal characteristics related to the shape, size, and concentration of soft matter constituents, although their development represents a difficult inverse problem. In this paper, we propose a numerical renormalization method that provides understanding of the contrast diffusion mechanism closely related to both the component hierarchy and the dynamic of molecular motion with a weak correlation with underlying structure. We demonstrate simulations of our method on a heterogeneous material with a self-similar random organization and show that we derive efficient temporal diffusion properties for disordered geometry, size and concentration of its components at different Euclidean dimensions. The proposed approach provides a tool for interpretation of experimental data obtained for meta- and native materials.

Keywords: magnetic resonance, signal attenuation, temporal diffusion.