Rusciano, Francesco (2023) Fickian non-Gaussian diffusion in glass-forming liquids. [Tesi di dottorato]

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Abstract

In 2009, ground-breaking experiments on nanometric beads in complex fluids revealed the existence of a novel type of diffusion (that is distinct from both standard and anomalous diffusion), characterized by a linear time-dependent mean square displacement and a non-Gaussian displacement distribution. In the past few years, many other examples of such a “Fickian yet non-Gaussian Diffusion”, (FnGD) have been reported in literature. FnGD is generically associated to some dynamical and/or structural heterogeneity of the environment. This feature motivated us to investigate the possible occurrence of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple models of molecular liquid [1, 2]. We here demonstrate that FnGD "strengthens" on approaching the glass transition, by identifying distinct timescales for Fickianity, τF, and for restoring of Gaussianity, τG, as well as their associated length-scales, ξF and ξG. We find τG ∝ τFγ, with γ > 1, for all investigated systems. In the deep FnGD regime, particle displacement distributions display exponential tails: we show that the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master-curve, l(t)/ξG ∝ (l(t)/ξG)^α with α ≃ 0.33. For the investigated glass-formers, this behaviour is independent from interaction potential and dimensionality [2]. We further discuss the connections of the time- and length-scales characterizing FnGD with structural relaxation and dynamic heterogeneity, through a complementary study of the dynamics in the reciprocal Fourier-space. Finally, we illustrate the connections between FnGD scales and standard timescales usually considered in the late relaxation of glass-forming liquids, showing that these timescales are always related, and for whatever system, by the same power-law relations. Overall, a number of universal scaling laws for very long-time single-particle dynamics (here reported for the first time) seem to emerge close to the glass transition, and characterize the Fickian non-Gaussian regime of glass-forming liquids. In conclusion, this work of thesis is at the crossroads between two major issues in soft matter, namely glass transition and the recently discovered Fickian yet non-Gaussian Diffusion (FnGD), and unveils strong connections between them.

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