Dynamic Slowdown in Glass-Forming Liquids

Updated 29 November 2025

Dynamic slowdown in glass-forming liquids is characterized by a steep increase in relaxation time and viscosity due to the growth of cooperatively rearranging regions.
Simulations and experiments reveal that dense-packed clusters and spatially correlated domains directly link microscopic structural changes to macroscopic dynamic behavior.
The interplay between local order, dynamic heterogeneity, and mechanical constraints establishes universal scaling laws that inform predictive models of glass transition.

Glass-forming liquids display a dramatic increase in structural relaxation time and viscosity when cooled or compressed towards the glass transition, with mobility decreasing by many orders of magnitude over a narrow temperature range. Despite the absence of clear static structural changes in simple two-point measures, the underlying microscopic mechanisms driving this slowdown have been traced to the emergence and growth of correlated domains, changes in dynamical heterogeneity, and the evolution of amorphous or locally ordered structures. Recent advances unify structural, dynamical, thermodynamic, and mechanical perspectives, highlighting the interplay of local packing, dynamic disorder, collective rearrangements, and barrier growth.

1. Microscopic Mechanisms of Dynamical Slowdown

The core mechanism underlying the slowdown in glass-forming liquids is the emergence of spatially correlated domains—cooperatively rearranging regions (CRRs)—whose size grows upon cooling, necessitating the collective movement of increasingly larger particle clusters for relaxation. In the regime of supercooling, particle motion becomes intermittently caged and relaxation proceeds via rare, collective hops, leading to a non-exponential decay of correlation functions and pronounced dynamical heterogeneity.

A key result from the local-density analysis (Li et al., 2015) identifies the spatial clustering of “dense-packed” environments as the structural origin: the top 13% of particles by local Voronoi density ρᵢ participate in clusters whose average size ⟨N_c⟩ (from the cluster-size distribution P(N_c)) defines a static length ξ = ⟨N_c⟩^{1/3} in 3D. As temperature decreases, these clusters grow in size while their overall fraction remains constant, forming percolating networks that relax anomalously slowly. The relaxation of these dense regions exhibits prolonged two-step plateau dynamics in overlap functions, directly linking cluster growth to macroscopic slowdown and dynamic heterogeneity.

Molecular-dynamics simulations reveal analogous processes in metallic glasses, where clusters of low-mobility atoms—identified via isoconfigurational mean-squared displacements—begin to coalesce and grow below a characteristic crossover temperature, accompanied by local chemical enrichment and increase in specific local order parameters (e.g., Cu-centered icosahedral motifs), further stabilizing slow regions (Puosi et al., 2017, Wong et al., 2017).

2. Quantitative Measures: Structural and Dynamic Length Scales

Several length scales track the evolution of dynamical slowdown:

Static length scales: Extracted via point-to-set correlations, order-agnostic amorphous overlap probes, or cluster analysis. In the colloidal confinement experiments, pinning boundaries induce static amorphous-order clusters of size ξ, measured via the equilibrium plateau of central region overlaps (Zhang et al., 2015). The point-to-set length ξ diverges as the system approaches the glass transition packing fraction or temperature, signaling the loss of configurational entropy and the onset of collective glassy states (Charbonneau et al., 2013, Tah et al., 2021).
Dynamic length scales: Defined via four-point dynamic susceptibility χ₄(t), whose peak and associated Ornstein–Zernike analysis of the four-point structure factor S₄(q,t*) yield the dynamic-heterogeneity length ξ₄ (Wong et al., 2017, Tah et al., 2017). In model systems, both ξ₄ and static amorphous lengths grow nearly synchronously in systems with medium-range crystalline order (MRCO), but may decouple in more generic, amorphous glass formers.
Universal scaling relations: The static length ξ extracted from dense-packed clusters or point-to-set correlation collapses onto a master curve when plotted against the α-relaxation time τα, following log(τα) ∼ ξ^ψ (cf. Vogel–Fulcher–Tammann and power-law scaling) (Li et al., 2015, Zhang et al., 2015, Adams et al., 2014). This collapse spans a wide range of densities, interaction potentials, and system types.

3. Dynamic Heterogeneity and Cooperative Rearrangement

Dynamical heterogeneity manifests as spatiotemporal regions where mobility is significantly lower or higher than the mean, quantified by measures such as the non-Gaussian parameter α₂(t) and four-point susceptibility χ₄(t) (Wang et al., 2017, Puosi et al., 2017, Puosi et al., 2019). The distribution of atomic or molecular mobilities becomes increasingly broad and intermittent, reflected in jump statistics (e.g., waiting-time distributions) that deviate from Poisson for T < T_c, with heavy tails and high randomness parameters R ≫ 1 (Saito, 14 May 2024, Kumar et al., 22 Nov 2025). As the temperature decreases, domains of slow mobility aggregate into clusters of growing size, whose relaxation requires cooperative motion in progressively higher-dimensional space of slow variables, further slowing dynamics and intensifying intermittency.

The emergence of cooperative rearrangements is further evidenced by direct species-resolved analysis in strong glass-forming networks such as silica, where the principal constraints on atomic jumps (e.g., fourth-nearest neighbor distances) vary by species, and the associated point-to-set lengths grow differently for silicon and oxygen (Kumar et al., 22 Nov 2025).

4. Thermodynamic and Entropic Constraints

Thermodynamic frameworks link the dynamical slowdown to reductions in configurational entropy. The Adam–Gibbs relation posits τ_α ∼ exp[const × ξ^ψ / k_B T], with the static length scale ξ reflecting the size of cooperatively rearranging regions and the configurational entropy loss as amorphous order grows (Zhang et al., 2015, Kob et al., 2014). Random First-Order Transition (RFOT) theory identifies this static length with the typical instanton size in a replica field theory, directly connecting point-to-set correlations and the dominant free-energy barrier to relaxation (Adams et al., 2014). In the presence of random pinning or boundary confinement, relaxation times exhibit an exponential dependence on pinning fraction c or cavity radius R, fully consistent with entropic depletion and barrier growth predicted by AG and RFOT models (Kob et al., 2014, Zhang et al., 2015).

Experimental breakdown of diffusivity-excess entropy scaling at well-defined packing fractions marks the onset of glassy slowdown, with abnormal translation-rotation coupling and rugged free-energy landscapes emerging once thermodynamic entropy no longer controls relaxation (Li et al., 2018).

5. Mechanical and Elastic Perspectives

Mechanical descriptions based on mesoscopic elasticity and local plasticity provide complementary insight into the slowdown. The characteristic local stiffness κ(T)—obtained by probing the inherent structure’s response to force dipoles—rises more rapidly than the macroscopic shear modulus G∞(T) on cooling, and in many systems, the structural relaxation barrier ΔE(T) is proportional to κ(T), yielding τ_α ∼ expA κ(T)/T. Limitations arise in network glasses or systems with granular potential-energy landscapes, where abundant low-barrier sub-basins uncouple κ(T) from relaxation.

Atomistic simulations identify localized plastic shear transformations as the mechanical events underlying relaxation; the residual plastic strength along soft directions in the inherent structure quantitatively predicts the location, time, and barrier of thermal rearrangements (Lerbinger et al., 2021). The scaling exponent β ≈ 4/3 links barriers to local strengths, and as temperature drops, barriers grow and dynamic correlations intensify.

6. Dynamic Slowdown: Universality and System Dependence

Across chemically distinct glass formers, universal features emerge in relaxation spectra, time–temperature superposition, and the temperature dependence of relaxation time, as evidenced by generic fields such as Randium (Pedersen, 4 Nov 2025). Time-scaled relaxation functions and dynamic heterogeneity master curves collapse universally when appropriately rescaled by system-dependent timescales set by dynamic heterogeneity or fragility (Wang et al., 2017). However, the microscopic mechanism—whether entropic, mechanical, or disorder-driven—retains system-specific features, such as the nature of slow variables in jump processes, the prevalence of MRCO, or the dimensionality of cooperative domains.

Tables below illustrate select key structural and dynamical length scales and their roles:

Length Scale	Physical Origin	Role in Slowdown
ξ (static, cluster)	Dense-packed cluster size, PTS	Controls τ_α via barrier
ξ₄ (dynamic)	χ₄(t) peak/OZ fit	Correlated domains of motion
φ₍ico₎ (icosahedral)	Voronoi local order, transient clusters	MRCO-mediated cooperativity
κ(T) (mesoscopic stiffness)	QLM response in inherent structure	Activation energy for rearrangement

7. Implications for Glass Transition Theories

The dynamic slowdown is rooted in the cooperative nature of relaxation, governed either by grown amorphous order (PTS length), entropic depletion (Adam–Gibbs/RFOT), or mechanical constraints (plastic strength, mesoscopic stiffness), depending on the system and interaction details. Fragility—a measure of how sharply τ_α increases on cooling—is empirically and theoretically tied to the static length growth and many-body local order: more fragile liquids display larger, faster-growing amorphous static lengths (Tah et al., 2021, Wang et al., 2017).

These findings establish that the super-Arrhenius slowdown of glass-forming liquids is accompanied by a rich structural evolution—whether in local density clusters, crystalline order, or amorphous-point-to-set correlations—with macroscopic kinetics tightly bound to microscopic collective processes. The elucidation of these connections provides predictive methodologies for assessing, controlling, and extracting relaxation properties in both simulations and experiments.