Intrinsic viscous liquid dynamics

TL;DR

The paper addresses the universality of viscous-liquid relaxation across glass-formers by introducing Randium, an energetically coarse-grained lattice model with a Gaussian interaction landscape and intrinsic, size-independent dynamics implemented via local swaps. Randium reproduces key experimental observations, including time-temperature superposition, a universal relaxation spectrum, and a parabolic scaling of the relaxation time with inverse temperature, while revealing emergent dynamic heterogeneity and a growing cooperative length scale $\xi$ that drives relaxation as $\tau\propto \exp(\xi)$. By matching molecular-liquid behavior to an extremely simple model, the work argues for a universal class of viscous-liquid dynamics governed by energy landscapes and dynamical facilitation, bridging detailed atomistic descriptions and coarse-grained theories. The findings provide a minimal, analytically tractable framework for understanding glassy relaxation and offer publicly available data and code to enable further exploration and generalization to other dimensions and connectivities.

Abstract

When liquids are cooled, their dynamics are slowed, and if crystallization is avoided, they will solidify into an amorphous structure referred to as a glass. Experiments show that chemically distinct glass-forming liquids have universal features of the spectrum and temperature dependence of the main structural relaxation. We introduce Randium, a generic energetically coarse-grained model of viscous liquids, and demonstrate that the intrinsic dynamics of viscous liquids emerges. These results suggest that Randium belongs to a universal class of systems whose dynamics capture the essential physics of viscous liquid relaxation, bridging microscopic molecular models and coarse-grained theoretical descriptions.

Figures (7)

• Figure 1: Illustration of the Randium model. The values inside each particle represent the particle type. The color of the line between neighbour particles represents the energy of that type-pair. For clarity, this figure shows an $8\times8$ lattice while the presented results are for a $192\times192$ lattice.
• Figure 2: (a) Overlap order-parameter, $Q(t)$, as a function of time for inverse temperatures ranging from $\beta=0.0$ (dark red) to $\beta=2.0$ (dark blue). A characteristic relaxation time, $\tau$, is defined as where the overlap order-parameter is $\frac{1}{2}$ (gray dashed). At high temperatures (reddish colors), the relaxation is near exponential (black dashed): $\exp(-t/t_0)$. At low temperatures (blueish colors), the relaxation is closer to a stretched exponential with exponent $\frac{1}{2}$ (red dashed): $A\exp(-\sqrt{t/t_0})$. The green-dashed is a high-temperature long-times prediction for $\beta=0$, see Eq. \ref{['eq:Qt_theory_longtime']}. (b) $1-Q(t)$ on a logarithmic scale.
• Figure 3: (a) The overlap order-parameter $Q(t/\tau)$ and (b) $\log(1-Q(t/\tau))$ as a function of scaled time. The orange dashed curve indicates a universal curve that $Q(t)$ approaches at intermediate and long times. For comparison, the red dashed is a stretch exponential: $Q=0.98\exp(\sqrt{t/t_0})$.
• Figure 4: Comparing the relaxation of Randium (orange dashed) with molecules measured by depolarized dynamic light scattering. The agreement is excellent.
• Figure 5: Temperature dependence of the relaxation time, $\tau(T)$. The red and green dashed lines is a prediction for the high temperature limit, see Appendix \ref{['sec:highT']}. The blue dashed line is a parabolic scaling Elmatad2009, $\tau_q\exp(J^2[\beta-\beta_q]^2)$, with $\tau_q=50(1)$, $J=4.3(1)$, $\beta_q=0.93(3)$. By extrapolating, the inverse glass-transition temperature is estimated to $\beta_g=2.16$ (defined as $\tau(\beta_g)=10^{14}$). The inset shows decoupling of two timescales, here half-life $\tau$ and self-diffusion $D$, at low temperatures ($\beta>1$).