Is Fickian Yet Non-Gaussian Diffusion Ubiquitous?

Abstract: Recent studies unveiled the Fickian yet non-Gaussian (FNG) dynamics of many soft matter systems and suggested this phenomenon as a general characteristic of the diffusion in complex fluids. In particular, it was shown that the distribution of particle displacements in Fickian diffusion is not necessarily Gaussian, and thus the Einstein and Smoluchowski theory describing the Brownian motion of individual objects in a fluid would not be applicable. In this Letter, we investigate whether the FNG dynamics so far reported in gels, granular materials, biological and active matter systems, is also a distinctive feature of colloidal liquid crystals. To this end, we perform Brownian Dynamics simulations of oblate and prolate colloidal particles in the nematic phase. We detect a normal and Gaussian dynamics at short and long time scales, whereas, at intermediate time scales, a non-Fickian and non-Gaussian dynamics is found. Additionally, we revisit the nature of the decay of the self-van Hove correlation function, $G_s(r,t)$, which is here approximated with an ellipsoidal, rather than spherical, Gaussian distribution. The new expression that we propose is able to correctly assess the Gaussian dynamics in inherently anisotropic systems, like liquid crystals, where the standard Gaussian approximation of $G_s(r,t)$ would fail.