Anomalous versus Fickian-but-Not-Gaussian Diffusion in Heterogeneous Systems Depends on the Time Scale of Observation

Both Fickian-but-not-Gaussian diffusion (FnGD) and anomalous diffusion have been observed in various heterogeneous systems. It remains unclear whether FnGD is an independent diffusion process and what factors determine whether anomalous diffusion or FnGD will be observed. Here, we studied two well-defined heterogeneous systems. The first system involves the simulation of polymer diffusion within polymer-nanoparticle mixtures (exhibiting temporal and population heterogeneity), and the second system involves single-molecule fluorescence tracking experiments of nanoparticle diffusion in inverse opals (exhibiting spatial heterogeneity). Despite the qualitative physical differences between these two systems, different types of diffusion, including anomalous diffusion, FnGD, and Brownian diffusion can emerge at varying time scales provided the system is ergodic. The observed phenomena are contingent upon the specific observation time window. Within the same system, diffusion that emerged at different time scales can be interpreted through different diffusion models. These observations suggest that future research should consider characterization across multiple time scales to fully elucidate the underlying mechanisms of heterogeneous systems.