Research ArticleCONDENSED MATTER PHYSICS

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

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Science Advances  12 May 2021:
Vol. 7, no. 20, eabe3392
DOI: 10.1126/sciadv.abe3392
  • Fig. 1 The system and structural characterization methods used in this work.

    (A) Snapshot of a 2D jammed amorphous bidisperse particle system. Scale bar, 100 μm. An arrow shows the direction of oscillating strain γ(t). (B) Oscillatory rheology also reported in Ref. (33). Connected symbols are measurements for the bidisperse systems considered in the Results, and unconnected symbols are measurements for the monodisperse systems mentioned in the Discussion and presented fully in the Supplementary Materials. (C) Schematic illustrating the environment matching method used to determine crystallinity. We identify neighbors, extract their environments, and then compare those environments to determine local structural homogeneity. (D) Visual rendering of a portion of a sample bidisperse experiment at γ0 = 0.068. Here, particles in crystalline grains of population greater than 1 are colored light blue. The inset is the radial distribution function collected over all particles during one cycle of the experiment, with the nearest-neighbor distance rcut marked in gray. (E) Visual rendering of the identical system snapshot with particles colored according to crystalline shielding Rnon−xtal. Disordered particles are colored purple. The inset is a histogram of Rnon−xtal collected over all particles during six cycles of the experiment.

  • Fig. 2 Global signatures of crystallinity and local neighborhood deformation as a function of strain amplitude γ0 show asymmetry with respect to shear direction.

    (A and C) Stroboscopic averages of local neighborhood deformation. The quantity ε is the eccentricity of the local neighborhood ellipse, and θ is its orientation. Error bars represent the standard error of the mean value at each time point. Increasingly dark colors correspond to increasing values of γ0. Values of γ0 for experiments at the lowest and highest strain amplitudes studied are shown. (B) Crystallinity in all systems, stroboscopically averaged. Error bars again represent the standard error of the mean value at each time point. Increasingly dark colors correspond to increasing values of γ0. Horizontal lines indicate the mean of each crystallinity signature. (D) Deviations in the crystallinity from its mean, ΔX(t), plotted against local neighborhood deformation ε(t) for example systems below and above yield. Shown are stroboscopically averaged quantities and corresponding error bars identical to those in (A) and (B). Light gray triangles mark all frames during the second shear half-cycle, for which θ(t) ≤ 90, and dark gray circles mark all frames during the first shear half-cycle, for which θ(t) > 90. (E) Two power spectral densities PX(ω) of nontransient crystallinity signatures as a function of γ0 for two distinct frequencies. The circles correspond to frequency ω*, which is the frequency of the needle oscillation; the squares correspond to frequency 2ω*, which is the second harmonic of the needle oscillation. Error bar estimation is described in the text.

  • Fig. 3 Correlations in crystallinity indicate individual particle rearrangement.

    (A) Rearrangement measurements p(s, ts,0) (top) and Dmin2(0,t) (bottom) for a sample experiment at γ0 = 0.068. Signals are shown as a function of t over one shear cycle, and t0 = 0 marks the beginning of the cycle. Results are shown as stroboscopic averages, and error bars represent the standard error of the mean value at each time point. Each signal represents a shielding level according to the color scheme detailed in Fig. 1, and is calculated over particles in the appropriate shielding level at t0. Colors of the least shielded (disordered) and most shielded layers are shown for reference. (B) Stroboscopically averaged Dmin2(0,t) as a function of stroboscopically averaged p(s, ts,0), for all strain amplitudes and all shielding layers. Error bars are standard errors of the mean in both dimensions.

  • Fig. 4 More shielded crystalline particles are more asymmetric in structural response with respect to shear direction.

    (A) Structural responses p(s, ts, t − 0.5) for particles at all shielding levels for experiments below (γ0 = 0.022) and above (γ0 = 0.068) yield, as solid and dotted lines, respectively. Stroboscopic averages are shown for clarity, and error bars denote the standard error of the mean value at each time point. (B) The ratio Pp(2ω*)/Pp(ω*) for all shielding layers as a function of γ0. Error bars are calculated via Taylor series propagation of the standard errors of the mean of each Pp(ω) quantity in the ratio. In both panels, signals are colored by shielding level according to the color scheme detailed in Fig. 1. Colors of the least shielded (disordered) and most shielded layers are shown for reference.

  • Fig. 5 Structural correlations for the system at γ0=0.157, the highest strain amplitude studied.

    (A) Structural autocorrelations p(s, ts,0) as a function of t over 1.5 shear cycles, with t0 = 0 marking the beginning of the cycle. Results are shown as stroboscopic averages, and error bars represent the standard error of the mean value at each time point. Each signal represents a shielding level according to the color scheme detailed in Fig. 1 and is calculated over particles in the appropriate shielding level at t0. Colors of the least shielded (disordered) and most shielded layers are shown for reference. (B) Full 2D distributions of p(s, ts, t0) for three shielding layers, shown beneath colored bars that indicate shielding level at time t0 according to the color scheme detailed in Fig. 1. Dark and light gray lines indicate times of strain extrema during each first and second half-cycle, respectively. Dotted lines indicate a 1D slice through each distribution at p(s, ts, t − 0.5).

Supplementary Materials

  • Supplementary Materials

    Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

    Erin G. Teich, K. Lawrence Galloway, Paulo E. Arratia, Danielle S. Bassett

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    • Sections S1 and S2
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