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Translational and rotational critical-like behaviors in the glass transition of colloidal ellipsoid monolayers

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Science Advances  15 Jan 2021:
Vol. 7, no. 3, eabd1958
DOI: 10.1126/sciadv.abd1958
  • Fig. 1 Properties and spatial correlations between fast (F), slow (S), and glassy (G) clusters and structural entropy ψS in translational (T) and rotational (R) motions.

    (A to H) Fast (∼8%), slow (∼8%), and glassy (∼30%) particles are shown in green, red, and yellow, respectively. The same video frame in (A) and (B) or (E) and (F) at ϕ = 0.81 for p = 2.3, and in (C) and (D) or (G) and (H) at ϕ = 0.74 for p = 6. (A and E) ST and (B and F) SR clusters are positively correlated with (A and B) GT clusters and (E and F) low ψST regions. (C and G) ST and (D and H) SR clusters are positively correlated with (C) GT and (D) GR clusters, and (G) low ψST and (H) low ψSθ regions. Translational and rotational motions in (C) and (D) are negatively correlated. Scale bars, 20 μm. (I) The cluster size fitted with NRgdf, where Rg is the radius of gyration. (J) The probability distribution of cluster sizes (symbols) fitted with 𝒫(N) ∼ N−μ exp ( − N/N0) (curves). p = 6 in (I) and (J). The SD of each data point calculated from different clusters or frames is smaller than the symbol size. (K) Locally favored close packing configurations.

  • Fig. 2 Critical-like behaviors of the dynamic CRRs.

    (A and D) The mean diameter ξ and (B and E) the size fluctuation χ (symbols) for (A and B) slow-moving (S) and (D and E) fast-moving (F) clusters in translational (T) and rotational (R) motions at different aspect ratios p = a/b. The curves are fitting functions ξF, S = ξ0[ϕ/(ϕc,0 − ϕ)]ν and χF, S = χ0[ϕ/(ϕc,0 − ϕ)]γ. The vertical solid and dotted lines mark the translational and rotational mode-coupling transition points ϕcT,θ, above which ξF and χF decrease. The error bars denote the SDs. (C and F) ξ and χ of (C) slow and (F) fast clusters at different p’s (symbols) collapse onto two master fitting lines ξF, S0 = [ϕ/(ϕc,0 − ϕ)]ν and χF, S0 = [ϕ/(ϕc,0 − ϕ)]γ. For slow clusters, ν = 1 and γ = 1.75 as in the 2D Ising universality class. Inset of (F): 1/ν and 1/γ for fast clusters increase linearly with the fragility index D for both translational and rotational motions. The fittings are within 5% errors.

  • Fig. 3 FFS analyses on structures.

    Aspect ratio p = a/b = 6.0. (A to D) The spatial correlations Cψ(r) of (A) the translational and (B) orientational glassy order parameters ψGT,θ, and (C) the translational and (D) orientational structural entropies ψST,θ. They are fitted by the 2D Ornstein-Zernike function: Cψ(r, L) ≅ r−1/4 exp ( − rψ(L)) (solid curves). (E and G) The fitted correlation lengths ξ(L) from (A) to (D) and other ϕ’s not shown in (A) to (D). (F and H) Fluctuations in ψ, i.e., χ(L). (E and F) ψGT,θ. (G and H) ψST,θ. All the orientational data in (F) are multiplied by a factor of 88 to collapse onto the translational data. Insets: The finite-size effects of ξ and χ fitted by ξ(L)/ξ( ∞ ) = exp [ − B1(ξ(L)/L)B2] and χ(L)/χ( ∞ ) = exp [ − B3(ξ(L)/L)B4]. B1 − 4 depends on p, but not on ϕ and the translational or rotational degree of freedom.

  • Fig. 4 Ising-like critical behaviors of structures.

    (A and D) The correlation length ξ( ∞ ) (symbols) and (B and E) fluctuation χ( ∞ ) (symbols) of (A and B) the local glassy order parameters ψGT,θ and (D and E) the local structural entropies ψST,θ at different aspect ratios p = a/b. The curves are fitting functions ξ = ξ0 · [ϕ/(ϕ0 − ϕ)] and χ = χ0 · [ϕ/(ϕ0 − ϕ)]7/4. ξ( ∞ ) and χ( ∞ ) of (C) ψGT,θ and (F) ψST,θ at different p’s (symbols) collapse onto two master fitting lines ξ = ξ0 · [ϕ/(ϕ0 − ϕ)] and χ = χ0 · [ϕ/(ϕ0 − ϕ)]7/4. The fittings are within 5% errors. The deviations of ξG,Sθ and χG,Sθ at p = 2.3 are due to the absence of nematic domains at small p so that the one-step glass transition is dictated by translational rather than rotational motion.

  • Fig. 5 Critical-like behaviors in the dynamics of structures.

    (A and B) The correlation function S(q, t) = 〈ψ(q, t)ψ( − q,0)〉 at different wave numbers q’s for (A) the GT order parameter ψGT at ϕ = 0.8 and (B) the orientational glassy order parameter ψGθ at ϕ = 0.7. Solid fitting curves for solid symbols: S(q, t) ∼ exp ( − t/τ(q)). Dashed fitting curves for open symbols: S(q, t) ∼ exp [ − (t/τ(q))β] with β < 1. (C) The decay time τ(q) (symbols) measured from (A) and (B) fitted with 1/[1 + (qξ)7/4] (curves). (A to C) Aspect ratio p = 6. (D) The lifetime of structural heterogeneities of ψGT,θ or ψST,θ, τ(q = 1/ξ, ϕ), against the structural relaxation time τα (symbols) at different p’s are fitted with [////ϕ/(ϕ0 − ϕ)]7/4 (lines). The fittings are within 5% errors. Simulation data are used here because the experimental time is shorter than τξ at high ϕ.

  • Table 1 Critical-like behaviors near ϕ0 and ϕc in the monolayers of colloidal ellipsoids.
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Supplementary Materials

  • Supplementary Materials

    Translational and rotational critical-like behaviors in the glass transition of colloidal ellipsoid monolayers

    Zhongyu Zheng, Ran Ni, Yuren Wang, Yilong Han

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    • Sections S1 to S6
    • Figs. S1 to S9
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