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Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
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http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4769256
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Figures

Image of FIG. 1.

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FIG. 1.

Self-part of the intermediate scattering function F s (k, t) of the component 1 particles for various glass-forming liquid models: (a) KALJ, (b) WAHN, (c) SS, and (d) NTW.

Image of FIG. 2.

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FIG. 2.

(a) α-relaxation time τα as a function of the inverse temperature T 0/T with the onset temperature T 0. (b) α-relaxation time τα as a function of the temperature difference (TT c )/T c from the mode-coupling divergence temperature T c . Each dashed line represents the power-law fits with exponent Δ = 2.4, 1.8, 2.2, and 2.8 for the KALJ, WAHN, SS, and NTW models, respectively.

Image of FIG. 3.

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FIG. 3.

Four-point dynamical susceptibility χ4(k, t) for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models.

Image of FIG. 4.

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FIG. 4.

Four-point static structure factor S 4(q, τα) at various temperatures as a function of the wave-number q for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models.

Image of FIG. 5.

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FIG. 5.

Scaled four-point static structure factor S 4(q, τα)/χ(τα) as a function of qξ(τα) at various temperatures for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models. The dashed line represents the Ornstein–Zernike form 1/(1 + (qξ(τα))α) with (a) α = 2.4, (b) 2.0, (c) 2.4, and (d) 1.5.

Image of FIG. 6.

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FIG. 6.

(a) Correlation length ξ(τα) as a function of (TT c )/T c . The dashed line represents the power-law behavior, ξ(τα) ∼ |TT c |−ν with ν = 0.5 (red) and ν = 0.25 (orange), respectively. (b) The relationship between the correlation length ξ(τα) and the α-relaxation time τα. The dashed line represents the power-law behavior, τα ∼ ξ(τα) z with z = 4.4 (red) and z = 11.0 (orange), respectively. (c) The dynamic susceptibility χ(τα) as a function of (TT c )/T c . The dashed line represents the power-law behavior, χ(τα) ∼ |TT c |−γ with ν = 1.2 (red) and ν = 0.37 (orange), respectively. (d) The relationship between the correlation length ξ(τα) and the dynamic susceptibility χ(τα). The dashed line represents the power-law behavior, χ(τα) ∼ ξ(τα)2−η with 2 − η = 2.4 (red) and 2 − η = 1.5 (orange), respectively.

Image of FIG. 7.

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FIG. 7.

Two-dimensional correlation maps of the three-time correlation functions ΔF 4(k, t 1, t 2, t 3) for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models. The state is chosen at the lowest temperature for each model as (a) T = 0.47, (b) T = 0.58, (c) Γ = 1.47, and (d) T = 0.32. The waiting times t 2 normalized by τα are increased from left to right in each model. The vertical (horizontal) dashed line denotes the α-relaxation time as t 1 = τα (t 3 = τα). Note that the waiting time is different in each figure.

Image of FIG. 8.

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FIG. 8.

The diagonal portions of the three-time correlation functions ΔF 4(k, t, t 2, t) for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models. The state is chosen at the lowest temperature for each model as (a) T = 0.47, (b) T = 0.58, (c) Γ = 1.47, and (d) T = 0.32. The waiting times t 2 are normalized by τα at each temperature.

Image of FIG. 9.

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FIG. 9.

Waiting time t 2 dependence of the integrated three-time correlation function Δhetero(k, t 2)/Δhetero(k, 0) for the (a) KALJ, (b) WAHN, (c) SS, and (d) NTW models. The waiting times are normalized by τα for each temperature. The solid curve is determined by a fitting with the stretched-exponential form exp [−(t 2hetero) c ] with c ≈ 0.6, 0.5, 0.5, and 0.3 for the KALJ, WAHN, SS, and NTW models, respectively.

Image of FIG. 10.

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FIG. 10.

(a) Average lifetime of DH τhetero normalized by the α-relaxation τα as a function of the inverse temperature T 0/T with the onset temperature T 0. The dashed line represents τhetero = τα as a viewing guide. (b) The relationship between two time scales, τhetero and τα. The dashed line is the power-law behavior τhetero ∼ τα ζ with a slope of ζ ≈ 1.9, 1.5, 1.25, and 0.9 from top to bottom.

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/content/aip/journal/jcp/138/12/10.1063/1.4769256
2013-01-02
2014-04-17

Abstract

We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob–Andersen, Wahnström, soft-sphere, and network-forming liquids. While the first three models act as fragile liquids exhibiting super-Arrhenius temperature dependence in their relaxation times, the last is a strong glass-former exhibiting Arrhenius behavior. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is characterized by various scaling relations that are analogous to the critical phenomena. We also examine how the growth of the length scale depends upon the model employed. Second, the four-point correlation function is extended to a three-time correlation function to characterize the temporal structures of the dynamic heterogeneities based on our previous studies [K. Kim and S. Saito, Phys. Rev. E79, 060501–R (Year: 2009)10.1103/PhysRevE.79.060501;K.Kim and S.Saito, J. Chem. Phys.133, 044511 (Year: 2010)10.1063/1.3464331]. We provide comprehensive numerical results obtained from the three-time correlation function for the above models. From these calculations, we examine the time scale of the dynamic heterogeneities and determine the associated lifetime in a consistent and systematic way. Our results indicate that the lifetime of the dynamical heterogeneities becomes much longer than the α-relaxation time determined from a two-point correlation function in fragile liquids. The decoupling between the two time scales is remarkable, particularly in supercooled states, and the time scales differ by more than an order of magnitude in a more fragile liquid. In contrast, the lifetime is shorter than the α-relaxation time in tetrahedral network-forming strong liquid, even at lower temperatures.

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Scitation: Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4769256
10.1063/1.4769256
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