Fickian yet non-Gaussian diffusion is not ubiquitous in soft matter

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, Gs(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 Gs(r, t) would fail.

Dynamics of Uniaxial-to-Biaxial Nematics Switching in Suspensions of Hard Cuboids

“…By definition, the self-dual shape is an intermediate geometry between prolate and oblate, where length (L), width (W ) and thickness (T ) are such that W = √ LT . Our simulations also confirmed the occurrence of a Fickian and Gaussian dynamics at both short and long times, thus providing an alternative picture to the claimed universality of Fickian yet non-Gaussian dynamics in soft-matter systems 41 . For its potential impact in nanotechnology, equally intriguing is the outof-equilibrium dynamics of cuboids, especially because it can spark phase switching and new material properties.…”

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels

“…For geometrical reasons, diffusion anisotropy becomes irrelevant in perfectly regular cubic lattices. One expects that any bias favouring displacements tangent to the available paths should become noticeable, either when dealing with anisotropic tracers or particles, 50 or in random networks with fractal paths, 40 which is the present case. Here we find that this effect is more significant in porous media where obstacle walls are thicker (as in the colloidal gel) because normal and tangent directions are more clearly differentiated (see Fig.…”

Cross-over in the dynamics of polymer confined between two liquids of different viscosity

“…For a system of identical particles royalsocietypublishing.org/journal/rsfs Interface Focus 9: 20180074 obeying the diffusion equation or in the ballistic regime with a velocity given by the Maxwell-Boltzmann distribution, the mean squared displacement of each particle increases linearly with time and the self-part of the van Hove self-correlation function has a Gaussian shape. In many soft matter systems however, it has been shown that the Gaussian approximation is not valid and that particles move either slower or faster than theoretically predicted [38][39][40]. We calculated G(r,Dt) for different time intervals Dt between 2.4 and 12t.…”