Fickian Non-Gaussian Diffusion in Glass-Forming Liquids
Francesco Rusciano, Raffaele Pastore, Francesco Greco
Abstract
Fickian yet non-Gaussian diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated with some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct timescales for Fickianity, ${\ensuremath{\tau}}_{F}$, and for restoring of Gaussianity, ${\ensuremath{\tau}}_{G}>{\ensuremath{\tau}}_{F}$, as well as their associated length scales, ${\ensuremath{\xi}}_{F}$ and ${\ensuremath{\xi}}_{G}$. We find ${\ensuremath{\tau}}_{G}\ensuremath{\propto}{\ensuremath{\tau}}_{F}^{\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\simeq}1.8$ for both systems. In the deep FnGD regime, the displacement distributions display exponential tails. We show that, in simulations, the time-dependent decay lengths $l(t)$ at different temperatures all collapse onto a power-law master curve $[l(t)/({\ensuremath{\xi}}_{G})]\ensuremath{\propto}(t/{\ensuremath{\tau}}_{G}{)}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=0.33$. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent $\ensuremath{\alpha}$. We further discuss the connections of the timescales and length scales characterizing FnGD with structural relaxation and dynamic heterogeneity.