Abstract
Fickian yet non-Gaussian diffusion is observed in several biological and soft matter systems, yet the underlying mechanisms behind the emergence of non-Gaussianity while retaining a linear mean square displacement remain speculative. Here, we characterize quantitatively the effect of spatial heterogeneities on the appearance of non-Gaussianity in Fickian diffusion. We study the diffusion of fluorescent colloidal particles in a matrix of micropillars having a range of structural configurations: from completely ordered to completely random. We show that non-Gaussianity emerges as a direct consequence of two coupled factors; individual particle diffusivities become spatially dependent in a heterogeneous randomly structured environment, and the spatial distribution of the particles varies significantly in such environments, further influencing the diffusivity of a single particle. The coupled mechanisms lead to a considerable non-Gaussian nature even due to weak disorder in the arrangement of the micropillars. A simple mathematical model validates our hypothesis that non-Gaussian yet Fickian diffusion in our system arises from the superstatistical behavior of the ensemble in a structurally heterogeneous environment. The two mechanisms identified here are relevant for many systems of crowded heterogeneous environments where non-Gaussian diffusion is frequently observed, for example in biological systems, polymers, gels and porous materials.
Highlights
Fickian yet non-Gaussian diffusion is observed in several biological and soft matter systems, yet the underlying mechanisms behind the emergence of non-Gaussianity while retaining a linear mean-square displacement remain speculative
Einstein’s theory of Brownian motion shows that for colloidal particles diffusing in two dimensions in a simple fluid, the mean-square displacement (MSD) is given by MSD = 4Dτ where D is the diffusion coefficient and τ is the lag time
In several cases diffusion has been observed to be Fickian but not Gaussian, that is, the MSD remains linear in time, but G( x) is not Gaussian
Summary
Fickian yet non-Gaussian diffusion is observed in several biological and soft matter systems, yet the underlying mechanisms behind the emergence of non-Gaussianity while retaining a linear mean-square displacement remain speculative. It was postulated that the differences in the local configurations of the larger matrix particles led to the observed Fickian yet non-Gaussian diffusion.
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