How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

TL;DR

This paper establishes a theoretical framework linking single-particle tracking and pulsed field gradient NMR methods for characterizing heterogeneous diffusion, demonstrating their relationship through analytical expressions and a two-region exchange model.

Contribution

It derives analytical relations between SPT and NMR diffusion measurements and applies them to a two-region exchange model, bridging the gap between the two techniques.

Findings

Derived analytical expressions for diffusivity distributions from SPT.

Linked SPT observables to NMR diffusion attenuation functions.

Validated the approach using a two-region exchange model.

Abstract

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived.