Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations

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 superArrhenius 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. E 79, 060501(R) (2009); J. Chem. Phys. 133, 044511 (2010)]. 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.

Universal rescaling of flow curves for yield-stress fluids close to jamming

“…Combined fits can even be made of the glass and jamming singularities [58][59]71], although this may influence an accurate determination of the separate rheological exponents. For glasses at rest (not included in the table) power-law relations between a heterogeneity length scale and well-separated microscopic time scales have been accurately established by simulations, with implied exponent ratios n/m = 1.5 and n/ν = 5.4 for soft spheres [81,82,84] and n/m = 1.75 for 2D colloids [83].…”

“…[12,[76][77][78][79][80]), both for glasses and jammed systems, and a detailed explanation is far beyond the scope of the present paper. For glasses at rest extensive simulations have been made from which both time scales could be recovered by analyzing the four-point dynamic correlation [81][82][83][84]. These simulations not only show the growing length and time scales but also their power-law interdependence.…”

Reduced strength and extent of dynamic heterogeneity in a strong glass former as compared to fragile glass formers

“…We note that the temperature where a plateau begins to emerge in F o (a; t) and F s (q; t) is approximately T = 0.5, and the emergence of the plateau has been identified as the onset temperature for slow dynamic in Refs. [15] and [23].…”

Decorrelation of the static and dynamic length scales in hard-sphere glass formers

“…Empirical correlations of one sort or the other have indeed been found with either the conventional scaling and a dynamic length [48][49][50][51][52] (with z varying from 2 to 5) or the activated expression and a dynamical [47,53,54] or a static length [9][10][11]14,25,39] (with ψ roughly varying from 1 to 2). Yet, as stressed by Harrowell and coworkers [55][56][57], correlation does not imply causation.…”