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Applicability of Dynamic Facilitation Theory to Binary Hard Disk Systems

Masaharu Isobe, Aaron S. Keys, David Chandler, and Juan P. Garrahan
Phys. Rev. Lett. 117, 145701 – Published 28 September 2016
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    Abstract

    We numerically investigate the applicability of dynamic facilitation (DF) theory for glass-forming binary hard disk systems where supercompression is controlled by pressure. By using novel efficient algorithms for hard disks, we are able to generate equilibrium supercompressed states in an additive nonequimolar binary mixture, where microcrystallization and size segregation do not emerge at high average packing fractions. Above an onset pressure where collective heterogeneous relaxation sets in, we find that relaxation times are well described by a “parabolic law” with pressure. We identify excitations, or soft spots, that give rise to structural relaxation and find that they are spatially localized, their average concentration decays exponentially with pressure, and their associated energy scale is logarithmic in the excitation size. These observations are consistent with the predictions of DF generalized to systems controlled by pressure rather than temperature.

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    • Received 15 April 2016

    DOI:https://doi.org/10.1103/PhysRevLett.117.145701

    © 2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Glass transition
    1. Physical Systems
    Granular monolayers
    1. Techniques
    Monte Carlo methods
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Masaharu Isobe*

    • Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, 466-8555, Japan

    Aaron S. Keys and David Chandler

    • Department of Chemistry, University of California, Berkeley, California 94720, USA

    Juan P. Garrahan

    • School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom

    • *isobe@nitech.ac.jp

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    Issue

    Vol. 117, Iss. 14 — 30 September 2016

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    Images

    • Figure 1
      Figure 1

      Phase diagram of hard disk binary mixtures [27] in terms of the EOS. Insets show examples of equilibrium configurations: for the nonequimolar mixture with (N,α,x1)=(32×32,1.4,1/3), we show a typical liquid configuration at ν=0.720, and a typical supercompressed configuration at ν=0.780. In contrast, for the equimolar mixture (N,α,x1)=(32×32,1.4,1/2), at ν=0.780, typical configurations show microcrystallization of 40% large disks immersed in the amorphous phase. Note that, when x1 is decreased below x1=1/3, microcrystallization of small disks emerges. Disks are colored by the number of nearest neighbors detected by a 2D version of the solid-angle based nearest-neighbor (SANN) algorithm [28] as 4 (orange), 5 (pink), 6 (green), 7 (blue), and 8 (dark blue). Disks belonging to a crystal cluster [29] are also indicated by a black perimeter.

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    • Figure 2
      Figure 2

      Averaged excitation indicator ⟨Ca(Δt)⟩ as a function of pressure p*−p0*, for several values of (a,Δt) used to define an excitation, for the system with (N,α,x1)=(64×64,1.4,1/3). The inset shows the dependence with a of the parameter κa obtained from fitting the data with Eq. (1). We also show a typical realization of the displacement field Di(Δt) for the choice (a/σ*,Δt)=(0.52,13.5) that illustrates dynamic heterogeneity in the system at the shown supercompressed conditions.

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    • Figure 3
      Figure 3

      Structural relaxation time ln(τα/τ0) as a function of p*−p0* for the nonequimolar mixture (N,α,x1)=(64×64,1.4,1/3) as extracted numerically (symbols). We also show a fit with Eq. (6) [dashed line; fitting parameters are p0*=17.6568(4), τ0=3.18, κ=0.241(4), λ=0.169(4)]. We also show the time scale that would be predicted by taking κ from the excitation data and using Eq. (6) (dotted-dashed line). For comparison with the supercompressed case, we show the data for the equimolar mixture (N,α,x1)=(32×32,1.11,1/2) which crystallizes at these conditions.

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