Understanding Flow Behaviors of Supercooled Liquids by Embodying Solid-Liquid Duality at Particle Level

TL;DR

The paper develops a microscopic framework to understand flow in supercooled liquids by introducing the local configurational relaxation time $τ_\mathrm{LC}$, which encodes dynamic heterogeneity and governs whether local regions respond as solids or liquids under shear. A universal, structure-driven relationship between $τ_\mathrm{LC}$ and the shear-affected relaxation time $τ_\mathrm{sh}$ is established, with $τ_\mathrm{sh}$ well described by an exponential form and master-curved under appropriate rescaling. The authors connect local structure to dynamics through specific spherical-harmonic features and use SVM/classification to reveal a structural basis for the solid–liquid duality, culminating in a shear-facilitated-activation model that merges local energy basins, tilt, and thermally activated escapes to predict steady and start-up rheology. The framework links microscopic packing and distortion to macroscopic flow, reproducing shear thinning and transient responses and offering a pathway to extend these ideas to other complex fluids and glasses.

Abstract

Understanding the flow behaviors of supercooled liquids presents a major challenge in liquid-state physics due to the strong nonlinearity and rich phenomena. To unravel this complexity, we introduce the concept of local configurational relaxation time $τ_\rm{LC}$, which allows us to embody the solid-liquid duality, proposed by Maxwell for phenomenologically describing materials' response to external load, at the particle level. The spatial distribution of $τ_\rm{LC}$ in flow is heterogeneous. Depending on the comparison between the local mobility measured by $τ_\rm{LC}$ and the external shear rate, the shear response of local regions is either solid-like or liquid-like. In this way, $τ_\rm{LC}$ plays a role similar to the Maxwell time. By applying this microscopic solid-liquid duality to different conditions of shear flow with a wide range of shear rates, we describe the emergence of shear thinning in steady shear, and predict the major characteristics of the transient response to start-up shear. Furthermore, we reveal a clear structural foundation for $τ_\rm{LC}$ and the solid-liquid duality associated with it by introducing an order parameter extracted from local configuration. Thus, we establish a framework that connects microscopic structure, dynamics, local mechanical response, and flow behaviors for supercooled liquids. Finally, we rationalize our framework in terms of activations from energy basins that are facilitated by shear. This model illustrates how local structure, convection and thermal activation collectively determine $τ_\rm{LC}$. Notably, it predicts two distinct response groups, which well correspond to the microscopic solid-liquid duality.

Figures (31)

• Figure 1: Shear viscosity $\eta$ as a function of shear rate $\dot{\gamma}$ for sample A (a) and sample B (b). Symbols denote the results obtained from MD data. Lines are to guide eyes. Three distinct rheological regimes can be delineated, as indicated by the vertical black dashed lines. In the shear-thinning regime, the relation can be described by a power law $\eta \sim \dot{\gamma}^{-\lambda}$.
• Figure 2: (a) Normalized distribution of $\tau_\mathrm{LC}$ ($H(\tau_\mathrm{LC})$) and $\tau_\mathrm{sh}$ ($H(\tau_\mathrm{sh})$) of sample A. (b) Normalized distribution of $\tau_\mathrm{LC}$ ($H(\tau_\mathrm{LC})$) and $\tau_\mathrm{sh}$ ($H(\tau_\mathrm{sh})$) of sample B. In both (a) and (b), $\tau_\mathrm{LC}$ is measured at equilibrium, while $\tau_\mathrm{sh}$ is measured under the start-up shear condition with $\dot{\gamma}=0.00025$ for sample A and $\dot{\gamma}=0.00011$ for sample B. (c) Snapshot of the spatial distribution of $\tau_\mathrm{LC}$ of sample B at equilibrium. (d) and (e) illustrate the hierarchical feature of the spatial distribution of $\tau_\mathrm{LC}$. (d) gives a slice of a fast cluster. It is seen that particles gradually become slower as the distance from the fast center grows. (e) gives a slice of a slow cluster. It is seen that particles gradually become faster as the distance from the slow center grows. Black arrows in (d) and (e) are to guide eyes, indicating that fast particles tend to "grow" from a fast center (d), and slow particles tend to "grow" from a slow center (e).
• Figure 3: (a) and (b) display the relations between $\tau_\mathrm{LC}$ and $\tau_\mathrm{sh}$, denoted as $\tau_\mathrm{sh}(\tau_\mathrm{LC})$, obtained from start-up shear with various $\dot{\gamma}$ for sample A and sample B, respectively. In both (a) and (b), symbols denote the results, thick black lines denote the reference condition of $\tau_\mathrm{sh}=\tau_\mathrm{LC}$, thin blue lines denote the exponential fits for data, the positions of red vertical bars denote the boundaries between fast and slow groups $\tau_\mathrm{LC,c}$, and the length of red vertical bars denotes the value of $\tau_2$. (c) and (d) display the boundaries between the fast and slow groups $\tau_\mathrm{LC,c}$ as a function of $\dot{\gamma}^{-1}$ for sample A and sample B, respectively. In both (c) and (d), symbols denote the results, dashed lines denote the linear fits to data points.
• Figure 4: (a) Slice of the spatial distribution of $\tau_\mathrm{LC}$ of sample A at equilibrium. (b) -- (d) Slices of the spatial distribution of $\tau_\mathrm{sh}$ of sample A obtained under start-up shear with various $\dot{\gamma}$ denoted at each panel. In (b) -- (d), white dashed lines denote the boundaries between fast and slow groups of particles found by equation \ref{['eq:divide_fast_slow']}. (e) -- (h) show the results for sample B.
• Figure 5: (a) and (b) show the transient stresses of the slow part, normalized by the corresponding stable-state stresses, under start-up shear with various $\dot{\gamma}$ for sample A and sample B, respectively. In both (a) and (b), we adopt $\gamma=\dot{\gamma}t$ as the time variable. (c) and (d) show the transient stresses of the fast part, normalized by the corresponding stable-state stresses, under start-up shear with different $\dot{\gamma}$ for sample A and sample B, respectively. In both (c) and (d), lines denote the fits with $\sigma^*(t) = 1 - \exp(-t/\tau_\mathrm{f})$.