Understanding Slow and Heterogeneous Dynamics in Model Supercooled Glass-Forming Liquids

Abstract

Glasses are ubiquitous in nature. Many common items such as ketchups, cosmetic products, toothpaste, etc. and metallic glasses are examples of such glassy materials whose dynamical and rheological properties matter in our daily life. The dynamics of these glass-forming systems are known to be very sluggish and heterogeneous, but a detailed understanding of the origin of such slowing down is still lacking. Slow heterogeneous dynamics occur in a wide variety of systems at scales ranging from microscopic to macroscopic. Polymeric liquids, granular material, such as powder and sand, gels, and foams and also metallic alloys show such complex glassy dynamics at appropriate conditions. Recently, the existence of dynamical heterogeneity has also been found in biological systems starting from collective cell migration in a monolayer of cells to embryonic morphogenesis, cancer invasion, and wound healing. Extensive research in the past decade or so lead to the understanding that there are growing dynamic and static correlation lengths associated with the observed dynamical heterogeneity and rapid rise in viscosity. In this review, we have highlighted the recent developments on measuring these correlation lengths in glass-forming liquids and their possible implications in the physics of the glass transition.

Figure 1

(a) Snapshot of two dimension simulation box of a binary Lennard-Jones mixture with each particle color coded with the amount of displacement it went through in the τ_α time scale (structural relaxation time). The existence of particles with different mobilities and their spatial correlation can be clearly seen with the clusters formed. (b) Distinct local cellular structural conditions lead to dynamic heterogeneity in two-dimensional dense biological tissue. (The image is customized with permission from ref (4). Copyright 2021 Royal Society of Chemistry). (c) Dynamical heterogeneity present in colloidal glass near the glass transition (adapted with permission from ref (5). Copyright 2016 American Chemical Society). (d) Snapshot of a two-dimension colloidal glass system with packing fraction ϕ = 0.631 and polydispersity δ = 9%, with the color code indicating the magnitude of the orientational order parameter Ψ̅₆ averaged over the structural relaxation time (τ_α) (adapted with permission from ref (6). Copyright 2007 American Physical Society).

Figure 2

(a) Schematic diagram for the block analysis method. (b) Time evolution of four point susceptibility (χ₄(t, T)) (see text for definition) for a binary Lennard-Jones system in three dimensions. The appearance of a peak in χ₄(t) at time closer to the structural relaxation time τ_α indicates the presence of maximal dynamic correlations at that time scale, and an increase in peak height (χ₄^P(T)) with decreasing temperature indicates the growth of dynamic correlations. (c) Finite size scaling done on χ₄^P(N,T) to obtain the dynamic heterogeneity length scale ξ_d^FSS(T). The system size variation of χ₄^P(N,T) for the system at different temperatures is plotted in the inset (adapted with permission from ref (13). Copyright 2009 Proceedings of the National Academy of Sciences of the United States of America). (d) Scaling collapse obtained for χ₄^P(L_B,T)/χ₄^P(∞,T) on rescaling the block length L_B with an appropriate system length scale ξ_d^Block. Also, the block size variation of χ₄^P for different temperatures is shown in the inset (adapted with permission from ref (19). Copyright 2017 American Physical Society). (e) Self-part of the van-Hove function, G(x, τ_α), calculated for a composite particle made of particles present in a block of linear length L_B at τ_α time. The non-Gaussianity of G(x, τ_α) for a smaller block size indicates the presence of different mobility clusters at the length scale of the block size (adapted with permission from ref (20). Copyright 2018 American Physical Society). (f) Comparison of the temperature dependence of the dynamic length scale obtained from FSS of χ₄^P(N,T), i.e. ξ_d^FSS, block length scaling of χ₄^P(L_B,T), i.e. ξ_d^Block, and block length scaling the non-Gaussian parameter of the self-part of the van-Hove function of a composite particle, i.e. ξ_d^Binder.

Figure 3

(a) Schematic of a rod-like particle as probe in a glassy environment. (b) Rod length variation of the peak value of non-normal parameter (α_3D^P), a parameter which quantifies the fluctuation in the rotation diffusion constant of the rod in a glassy environment modeled by the 3dKA system. The time evolution of α_3D for a rod of length L = 2.5 immersed in the same model system is presented in the inset. (c) Collapse obtained for α_3D^P(T) on scaling the rod length with an appropriate system length scale, ξ_rod(T). The quality of collapse and the comparison of the obtained length scale with the dynamic length scale measured by traditional methods in the inset confirms the robustness of the method. (d) Distribution of log of scaled first passage time (FPT) distribution (scaled with moment of inertia) for rods of various lengths in the 3dKA system at temperature T = 2.0 (high temperature) with the absorbing boundary at ϕ = π/8. (e) Same distribution but at temperature T = 0.5 (low temperature). The emergence of supercooling effects can be seen clearly as a shoulder build up in a small time regime indicating the cooperative motion because of emerging local structure. (f) Rod length scaling done on the skewness of P(log(t)), i.e. χ_FPT(T, L_rod), to obtain a collapse. The obtained length scale ξ_Rod^S is compared with the PTS length scale, the static length scale obtained from FSS of τ_α (ξ_PTS+FSS^S), and the static length scale obtained from block length scaling of χ_τ(L_B, T)/χ_τ(∞, T) (see text for definition). (The inset is adapted with permission from ref (13). Copyright 2009 Proceedings of the National Academy of Sciences of the United States of America and with permission from ref (20). Copyright 2018 American Physical Society and all of the analysis on the rod system is adapted from ref (21)).

Figure 4

(a) Structural motifs at the deep supercooled regime, defective icosahedra (green, top right structure), and full icosahedra (purple, bottom right structure) (adapted with permission from ref (24). Copyright 2018 Springer Nature). (b) Snapshots of local ordering in liquids close to the glass transition temperature, T_g. Red particles are the locally favored structure (particles with high hexatic order) spontaneously formed in a sea of normal liquid (adapted with permission from ref (12). Copyright 2018 American Physical Society). (c) Different types of structural ordering (between short-range localized ordering (denoted by particle size a), medium-range crystal ordering (denoted by MRCO), and particular bond orientational ordering (denoted by icosahedral LFS)) for 2d spin liquids and 3d polydisperse colloids (adapted with permission from ref (25). Copyright 2013 Royal Society of Chemistry). (d) Molecular snapshot for generic glass formers close to T_g (adapted with permission from ref (12). Copyright 2018 American Physical Society). (e) Growth of dynamic (S₄(q, τ_α), S₄(q, τ_b), BC) and static length scales (ξ_pts, τ_α, λ_min) for molecular liquid in the presence of medium range crystalline order (MRCO), and ξ₆ is the structural length scale, which emerges from local structural order (adapted with permission from ref (12). Copyright 2018 American Physical Society). (f) Growth of dynamic and static length scales for generic glass forming liquid (adapted with permission from ref (12). Copyright 2018 American Physical Society).