NMR measurement and Brownian movement in the short-time limit

Abstract

This study is carried out to find relations between the time-dependent molecular self-diffusion and the attenuation of NMR spin-echo. Two cases of diffusion are considered: the Brownian motion in Ornstein's short-time limit and the random walk with memory [13]. The friction and the correlation time describe the mechanism of entrapping interactions between molecules or their bonding to macromolecule chains. The obtained formula for the self-diffusion attenuation is valid at short times and it develops into the well-known Torrey's result in the long-time limit. It fits very efficiently into the NMR data from Refs. [19–20].