A minimal model for kinetic arrest

Abstract

To elucidate slow dynamics in glassy materials, we introduce the {\it Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure-8. This system undergoes kinetic arrest at a critical packing fraction $\varphi ={\varphi }_g<1$, and for $\varphi \approx {\varphi }_g$ long-time diffusion is controlled by rare, cooperative `junction-crossing' particle rearrangements. We find that the average time between junction crossings ${\tau }_{JC}$, and hence the structural relaxation time, does not simply scale with the configurational volume $\OmegaLow$ of transition states, because ${\tau }_{JC}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.

4 pages, 4 figures

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Cited by in corpus (5)

• Cooperative Strings and Glassy Interfaces
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
• A Free Energy Landscape for Cage Breaking of Three Hard Disks
• Lattice Model of Glasses
• Quasi-One Dimensional Models for Glassy Dynamics