Unveiling Structural Bottlenecks of Dynamic Disorder in a Density-Tunable Glass Former: From Strong to Fragile Regimes

Abstract: Fragility characterizes how rapidly a glass-forming liquid slows down upon supercooling, but whether strong and fragile behaviors arise from the same microscopic relaxation mechanism remains unclear. Here, we address this question using a density-tunable soft-repulsive binary mixture spanning distinct fragility regimes and analyze particle jump dynamics within the framework of dynamic disorder. Across these regimes, we show that increasing fragility leads to progressively broader cage-lifetime distributions and increasingly non-exponential survival probabilities, revealing non-Poisson cage-to-jump statistics governed by fluctuating jump rates and slowly evolving structural variables. To characterize their structural origin, we first identify the neighbor ranks most strongly coupled to jump motion using Kullback-Leibler divergence and Pearson correlation analyses. We then introduce a structural slowness parameter that combines these neighbor-distance fluctuations into a reduced slow coordinate for constructing the slow-fluctuation survival probability. A comparison with the actual survival probability shows that localized neighbor-distance fluctuations control the jump rate in the strong regime, whereas extended neighbor rearrangements become relevant in the intermediate and fragile regimes, increasing the effective dimensionality of the slow-variable space. In the fragile regime, distance-based descriptors alone become insufficient at the lowest temperature, where the Voronoi free volume captures additional cage-volume fluctuations in the rate-controlling slow variable. Point-to-set correlations grow with fragility, but the spatial extent of the slow variables exceeds the point-to-set length. These results show that fragility changes the structural bottleneck for microscopic rate fluctuations, linking dynamic disorder and multidimensional slow variables.

• The paper demonstrates that tuning density modulates fragility by transitioning from localized, distance-based constraints in strong regimes to extended, packing-sensitive variables in fragile states.
• The methodology employs large-scale molecular dynamics to quantify particle jumps and cage statistics, revealing non-Poissonian dynamics in supercooled liquids.
• Structural slowness parameters combining neighbor distances and free volume elucidate complex collective constraints that challenge conventional static measures.

Microscopic Mechanisms of Dynamic Disorder in Density-Tunable Glass Formers Across Fragility Regimes

Introduction

The fragility of glass-forming liquids, quantifying the sensitivity of relaxation times to supercooling, remains a pivotal concept in the physics of disordered materials. However, the microscopic origin of the strong-fragile dichotomy is actively debated, particularly whether distinct fragility regimes arise from universal or fundamentally different local relaxation mechanisms. This study presents a comprehensive analysis of relaxation dynamics in a soft-repulsive binary mixture where fragility can be tuned continuously via density, facilitating a controlled exploration of relaxation processes without changing chemical topology or bonding geometries (2607.04870).

Simulation Methodology and Model System

The model employed is a three-dimensional, equimolar binary mixture with purely repulsive harmonic interactions and tunable number density $\rho$ in the range $0.65 \leq \rho \leq 0.82$, allowing access to strong, intermediate, and fragile dynamical regimes at fixed composition. The system is simulated using large-scale molecular dynamics (N = 10,000), utilizing LAMMPS with carefully controlled equilibration and production phases spanning both normal liquid and deeply supercooled states. At each state point, relaxation dynamics are quantified through the self-overlap function and the corresponding structural relaxation time $\tau_\alpha$, the temperature dependence of which is analyzed using the Vogel-Fulcher-Tammann relation to extract kinetic fragility indices.

Local Relaxation: Particle Jump Analysis and Cage Statistics

Structural relaxation is parsed into sequences of particle 'jumps,' representing intermittent cage escape events. Jump events are operationally detected using a hop function $h(t)$ based on time-averaged local displacements, with thresholds selected via cumulative hop amplitude distributions. This hop-based decomposition enables direct measurement of residence times in cage and jump states, as well as the statistics of waiting times, facilitating a high-fidelity probe of dynamical heterogeneity and temporal intermittency.

Across all densities, the distribution of jump-state residence times remains rapidly decaying and only weakly temperature dependent, with broadening at lower densities attributed to weaker local packing constraints. In marked contrast, the distribution of cage-state residence times, $W_\text{cage}(t)$, exhibits strong non-exponential broadening with decreasing temperature; this effect is significantly more pronounced in the fragile regime, where the distribution develops extensive long-time tails and the randomness parameter $R$—quantifying deviations from Poisson (Markovian) statistics—grows sharply at low temperature. The stretching exponent $\beta$ characterizing the non-exponential survival probability $C_s(t)$ likewise distinguishes strong (gradual decrease of $\beta$) and fragile (abrupt decrease) regimes. The data substantiate that the onset and degree of temporal heterogeneity are systematically linked to fragility.

Structural Origins of Dynamic Disorder: SSP Construction

To elucidate the local structural origin of non-Poissonian cage statistics and dynamic disorder, the analysis employs information-theoretic and correlation-based metrics—specifically, Kullback-Leibler (KL) divergence $D_\text{eq}(k)$ and Pearson correlation coefficient $0.65 \leq \rho \leq 0.82$0—applied to neighbor-distance distributions as a function of jump proximity. These diagnostics consistently identify that the neighbor ranks (including particles at varying radii from the central particle) significantly affecting the likelihood of a jump differ across fragility regimes:

• Strong regime: Only a localized set of outer first-shell and onset-of-second-shell neighbors modulate the jump rates. These fluctuations remain spatially confined over the entire supercooled window.
• Intermediate regime: Additional neighbor ranks, extending deeper into the second shell and even farther, become relevant upon cooling, increasing the operational dimensionality of rate-controlling variables.
• Fragile regime: A highly extended set of neighbor ranks spanning the first and second shells governs the rate. Furthermore, at the lowest temperatures, neighbor-distance fluctuations alone fail to fully capture rate fluctuations; inclusion of Voronoi free volume as an additional variable is needed to account for cage-volume fluctuations.

These findings inform the construction of a Structural Slowness Parameter (SSP), a reduced (often multidimensional) slow coordinate blending critical neighbor-distance fluctuations (and, in fragile cases, free volume) into a surrogate variable for modulating the jump rate in survival probability analysis.

Dynamic Survival Probability: Beyond Poissonian Dynamics

The non-Markovian nature of relaxation is rigorously addressed via a dynamic-disorder framework, wherein $0.65 \leq \rho \leq 0.82$1 is formally derived as a sum—or convolution—over substates with distinct, quasi-static jump rates, determined by the slow variables (SSP/free volume). The slow-fluctuation survival probability computed with appropriately chosen SSPs provides an excellent match to the observed survival probabilities, with accuracy contingent on the inclusion of the experimentally identified set of structural variables. Notably:

• In strong regimes, a compact SSP constructed from a limited set of neighbor ranks suffices.
• In intermediate and fragile regimes, extended SSPs spanning many neighbor ranks are essential.
• In the fragile regime and for the smaller particle species, a two-dimensional slow variable combining neighbor distances and free volume is required to reproduce observed long-lived rate fluctuations.

These results contradict any single-variable or strictly local description of dynamics in the fragile regime, emphasizing the emergence of complex, collective constraints.

Relation to Static Amorphous Order: Point-to-Set Correlations

Point-to-set (PTS) correlations are used to quantify the spatial extent of static amorphous order, providing a static correlation length $0.65 \leq \rho \leq 0.82$2 via cavity-overlap measurements. $0.65 \leq \rho \leq 0.82$3 manifests only limited growth upon cooling in strong regimes but grows rapidly and continuously in fragile regimes, corroborating earlier work on the same model. However, direct comparison shows that the spatial extent of the rate-controlling slow variables—especially in the fragile regime—significantly exceeds $0.65 \leq \rho \leq 0.82$4, and likewise remains smaller than the dynamic correlation length $0.65 \leq \rho \leq 0.82$5 (collective heterogeneity scale). This reveals that dynamic disorder is coupled to structural fluctuations not fully captured by PTS-based measures, and the spatial scale of rate modulation is distinct from both static and dynamic length scales previously considered.

Numerical Results and Strong Claims

• The increase of the dimensionless free-energy barrier along the hop coordinate becomes much more pronounced with increasing fragility; in the fragile regime, the barrier increases almost three-fold upon cooling from the highest to the lowest temperature studied.
• Randomness parameter $0.65 \leq \rho \leq 0.82$6 shows sharply accelerated growth in the fragile regime, with values exceeding those of strong liquids by a large margin at low temperatures.
• At the lowest temperatures, distance-based SSPs alone fail (confirmed for particle A) to explain survival probability in the fragile regime; augmenting with Voronoi free volume resolves the deficit, rigorously demonstrating the necessity of joint distance and packing descriptors.
• The decoupling between the operational spatial extent of slow variables and $0.65 \leq \rho \leq 0.82$7 is explicitly confirmed, unlike previously reported close correspondences for models of silica and KALJ mixtures.

Theoretical and Practical Implications

This work decisively demonstrates that the microscopic origin of dynamic disorder, and hence the mechanism of slow relaxation, evolves systematically with fragility: from localized, purely distance-based constraints in strong liquids to spatially extended, packing-sensitive, multidimensional slow variables in fragile ones. The necessity of multiple structural descriptors for fragile glass formers contradicts universal one-variable or single-shell pictures and suggests that machine-learned or theory-driven order parameters used for predicting dynamics must explicitly adapt to the regime of fragility and local interaction potential.

On a practical level, the methodology and diagnostic framework applied here—selective construction of slow variables via mutual information and survival probability matching—provide transferable tools for analyzing other glass-forming systems, driven liquids, or systems virtue to rare event kinetics (e.g., superionic glassy electrolytes, biomolecules, confined fluids).

Outlook and Future Directions

The current findings prompt several targeted future investigations:

• Developing and validating genuinely multidimensional, system-specific slow variables using advanced data-driven (ML) approaches in fragile glasses.
• Directly probing the energetic landscape underpinning multidimensional rate-modulating constraints.
• Extending analyses to other interaction potentials or mixed-bonding systems to determine universality versus specificity in the fragility dependence of relaxation mechanisms.
• Bridging the operational slow-variable spatial extent with experimentally accessible observables (e.g., via nonlinear response or local elasticity measurements).

Conclusion

This study establishes that the strong-to-fragile crossover in glass-forming liquids is accompanied by a qualitative transformation in both the spatial extent and the nature of the slow variables governing dynamic disorder in microscopic jump rates. The transition from localized, distance-based slow variables to extended, packing-sensitive, multidimensional constraints in fragile systems is directly demonstrated, and found to exceed the static amorphous order length scale as measured by point-to-set correlations. These results provide a quantitative framework for the microscopic sources of dynamic heterogeneity in glass formation, with significant implications for theoretical modeling, interpretation of experimental data, and the rational design of amorphous materials with tailored kinetic properties.