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

Area of Science:

• Physical Chemistry
• Materials Science
• Statistical Mechanics

Background:

• Heterogeneous systems exhibit complex diffusion behaviors like Fickian-but-not-Gaussian diffusion (FnGD) and anomalous diffusion.
• The relationship between FnGD and anomalous diffusion, and the factors governing their emergence, remain poorly understood.

Purpose of the Study:

• To investigate whether FnGD is an independent diffusion process.
• To determine the factors influencing the observation of anomalous diffusion versus FnGD.
• To explore diffusion dynamics in well-defined heterogeneous systems across multiple time scales.

Main Methods:

• Computational simulation of polymer diffusion in polymer-nanoparticle mixtures.
• Experimental single-molecule fluorescence tracking of nanoparticle diffusion in inverse opals.
• Analysis of diffusion behavior across different observation time windows.

Main Results:

• Both simulated and experimental systems demonstrated that anomalous diffusion, FnGD, and Brownian diffusion can emerge depending on the observation time scale.
• The observed diffusion behavior is contingent upon the chosen observation time window.
• Different diffusion models can describe phenomena observed at different time scales within the same system.

Conclusions:

• Diffusion behavior in heterogeneous systems is highly dependent on the observation time scale.
• FnGD and anomalous diffusion are not mutually exclusive and can be manifestations of the same underlying process observed over different time scales.
• Future studies should incorporate multi-time scale characterization to fully understand heterogeneous diffusion.