Surface-to-volume ratio with oscillating gradients

TL;DR

This paper derives a universal high-frequency behavior of the diffusion coefficient related to surface-to-volume ratio, enabling structural analysis of complex samples via NMR with oscillating gradients.

Contribution

It provides an exact formula for diffusion behavior at high frequencies and links different diffusion metrics, enhancing NMR-based structural characterization methods.

Findings

Derived universal high-frequency diffusion behavior

Linked various diffusion metrics

Outlined methods for arbitrary gradient waveforms

Abstract

Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This frequency dependence can be applied to quantify structure of complex samples with NMR using oscillating field gradients and static-gradient CPMG. We also demonstrate the inter-relations between different equivalent diffusion metrics, and describe how to calculate the effect of restrictions for arbitrary gradient waveforms.