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

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