The emergence of cooperativity accompanying vitrification: Insights from density fluctuation dynamics

Abstract

We discuss the emergence and growth of the cooperativity accompanying vitrification based on the density fluctuation dynamics for fragile glass-forming liquids. (i) The relaxation of density fluctuations proceeds by the particle (density) exchange process, and is diffusive; that is, the allowable kinetic paths are strongly restricted by the local conservation law. (ii) In normal liquid states, this exchange process is less cooperative, and the diffusion coefficient of density fluctuations $D_c$ is given as $D_c\sim {\lambda }^2/{\tau }_{\alpha }$, where $\lambda$ is the particle size and ${\tau }_{\alpha }$ is the structural relaxation time. On the other hand, in supercooled states the restriction on the kinetic path is more severe with increasing the degree of supercooling, which makes the exchange process more cooperative, resulting in $D_c\sim {\xi }_{\mathrm{d}}^2/{\tau }_{\alpha }$ with ${\xi }_{\mathrm{d}}$ being the cooperative length scale. (iii) The molecular dynamics simulation results show that the self-diffusion coefficient of the tagged particle, $D_s$, almost coincides with $D_c$, suggesting that the collective density diffusion and the particle diffusion closely share the same mechanism: in normal states $D_s$ determines $D_c$, but vice versa in supercooled states. This immediately leads to the idea that the breakdown of the Stokes-Einstein relation is not the anomaly in the single-particle dynamics but reflects the increase in the cooperativity in the density diffusion at the length scale of ${\xi }_{\mathrm{d}}$.

14 pages, 6 figures. This is the version of the article before peer review or editing, as submitted by an author to Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1742-5468/ab2ad0

References in corpus (4)

• Theoretical perspective on the glass transition and amorphous materials
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Finite size effects in the dynamics of glass-forming liquids
• Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities

Cited by in corpus (1)

• Solid-that-flows picture of glass-forming liquids