Discriminating stochastic processes for the assessment of materials properties by diffusion measurements

Assessing the materials properties of complex media, <i>e.g.</i> colloidal suspensions or intracellular fluids, frequently relies on quantifying the diffusive motion of tracer particles. In particular, from the particles' mean squared displacement (MSD) one may infer the complex shear modulus of the medium. Yet, experimentally the same power-law forms of the MSDs emerge for tracer diffusion in very different environments. For example, diffusive motion in a static maze of fractal obstacles (obstructed diffusion, OD) and motion in viscoelastic fluids (often described by fractional Brownian motion, FBM) can show an identical sublinear MSD scaling, but an MSD-derived complex shear modulus is meaningless for OD as the system does not feature any viscoelasticity. Here we show that OD and FBM trajectories are highly similar in many observables, including the MSD and the autocovariance function that reports on the memory of the particle motion. The Gaussianity and/or the asphericity of trajectories, extracted with single-particle tracking, allows for a proper discrimination of OD and FBM, facilitating a meaningful interpretation of the materials properties of the medium. In contrast, techniques that only monitor particle number fluctuations in a region of interest are not capable of discriminating highly similar random processes like FBM and OD as they only rely on the MSD. We therefore highly recommend the use of the more informative tracking of single particles when aiming to asses materials properties of the medium under investigation.