Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Abstract

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a “universal” evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

“…Quite often, the anomalous behavior is only transient, meaning the MSD is diffusive or ballistic at relatively short times, then it transitions to anomalous diffusion (subdiffusion or superdiffusion) and entails entirely Fickian diffusion at longer time scales. Anomalous diffusion in passive BM has been observed in soft biological systems [7][8][9][10][11][12], supercooled and ionic liquids [13][14][15][16][17][18], granular and glassy materials [19][20][21][22][23][24][25][26][27], colloidal suspensions [28,29], as well as diffusion under random external fields [30,31]. In active motion, anomalous diffusion has been reported in cell motion [32], chemically powered nanomotors [33], and even mammal movement [34].…”