Abstract
Dynamic heterogeneity, believed to be one of the hallmarks of the dynamics of supercooled liquids, is expected to affect the diffusion of the particles comprising the liquid. We have carried out extensive molecular dynamics simulations of two model glass-forming liquids in three dimensions to study the time scales at which Fick's law of diffusion starts to set in. We have identified two different Fickian times cales: one at which the mean squared displacement begins to show a linear dependence on time, and another one at which the distribution of particle displacements becomes Gaussian. These two times scales are found to be very different from each other and from the $\alpha$ relaxation time in both systems. An interesting connection is found between one of these Fickian time scales and the time scale obtained from the bond-breakage correlation function. We discuss the relation among these different times cales and their connection to dynamic heterogeneity in the system.
Highlights
One of the important unsolved problems in condensed matter physics is to understand the complex dynamics of supercooled liquids near the glass transition
The primary objective of this study is to estimate the time scales τD, τF, and τH in different generic glass-forming liquids and to compare them with other well-known important time scales in the system, such as the α-relaxation time τα and the bondbreakage time scale τBB We have looked for the existence of correlations among these different time scales and tried to figure out their consequence in understanding the dynamics of glass forming liquids approaching the glass transition
We show below the results for only one type of particle
Summary
One of the important unsolved problems in condensed matter physics is to understand the complex dynamics of supercooled liquids near the glass transition. In the last several decades, immense efforts have been made to understand the rapid rise of the viscosity and the slowing down of the dynamics of supercooled liquids as the glass transition is approached [1,2,3,4,5,6,7,8,9,10,11,12]. It is well-accepted that the slow dynamics become increasingly heterogeneous near the glass transition. In an earlier study [15], it has been shown that the lifetime of dynamic heterogeneity grows faster than the α-relaxation time, whereas in some other works [16,17,18,19,20], the ratio of this time scale with the α-relaxation time is found to depend sensitively on the temperature
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