Jamming Transition in Amorphous Materials Under Cyclic Shear: Evidence for a First-Order Transition with Quenched Disorder

Core Concepts

Jamming in cyclically sheared amorphous materials exhibits characteristics of a first-order phase transition with quenched disorder, primarily driven by fluctuations in the jamming density of finite-sized systems.

Abstract

Bibliographic Information:

Deng, Y., Pan, D., & Jin, Y. (2024). Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations. arXiv preprint arXiv:2403.01834v4.

Research Objective:

This research paper investigates the nature of the jamming transition in amorphous materials subjected to cyclic athermal quasistatic shear (CAQS). The authors aim to resolve the debate surrounding the classification of the jamming transition as either a first-order or second-order transition.

Methodology:

The researchers employ numerical simulations of standard models of soft, frictionless particles in two and three dimensions. They apply CAQS protocols to generate ensembles of jammed and unjammed states near the jamming transition density. By analyzing the probability distribution of the coordination number, finite-size scaling behavior of the jamming fraction, and the relationship between connected and disconnected susceptibilities, they provide evidence for their hypothesis.

Key Findings:

• The study identifies four distinct states in the system: unjammed, jammed, partially crystallized, and fragile states.
• Fragile states, characterized by low potential energy but unstable force networks, are deemed mechanically unstable and grouped with unjammed states.
• The jamming fraction exhibits a scaling behavior consistent with a first-order transition with quenched disorder, where fluctuations in the jamming density dominate.
• A square relationship between disconnected and connected susceptibilities further supports the presence of a first-order transition with quenched disorder.

Main Conclusions:

The authors conclude that the jamming transition in cyclically sheared amorphous materials is a first-order transition with quenched disorder. This conclusion challenges previous interpretations based on criticality and hyperuniformity. The study suggests that the jamming transition can be better understood within the theoretical framework of the athermally driven random-field Ising model.

Significance:

This research provides new insights into the fundamental nature of the jamming transition, a phenomenon observed in various physical systems. By establishing its classification as a first-order transition with quenched disorder, the study paves the way for a more accurate theoretical description and modeling of jamming in amorphous materials.

Limitations and Future Research:

The study focuses on a specific type of shear protocol (CAQS) and idealized particle models (soft, frictionless). Further research is needed to investigate the impact of different shear protocols, particle properties (e.g., friction, shape), and system dimensionality on the nature of the jamming transition. Additionally, exploring the connection between the observed first-order transition with quenched disorder and the Gardner phase in hard-sphere glasses could provide valuable insights.

Stats

The jamming density (J-point density) for the 2D model is approximately 0.842 - 0.843.
The maximum protocol-dependent jamming density obtained through cyclic athermal quasistatic compression (CAQC) is approximately 0.8465.
The asymptotic jamming density in the thermodynamic limit (N →∞) is determined to be φ∞J = 0.8432(2).
The average coordination number of jammed states (Z∗J) is approximately 4.1.

Quotes

Key Insights Distilled From

Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations

by Yue Deng, De... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2403.01834.pdf

Deeper Inquiries

How would the inclusion of frictional forces between particles influence the nature of the jamming transition and the stability of fragile states?

Introducing frictional forces between particles would significantly impact the jamming transition and the stability of fragile states. Here's how:
Impact on the Jamming Transition:

Shift in Jamming Density: Friction allows particles to resist sliding past each other, leading to mechanical stability at lower coordination numbers. This would result in a lower jamming density (φJ) compared to frictionless systems.
Modified Isostaticity: The isostatic condition, which dictates the minimum coordination number (Ziso) for marginal stability, would change. In frictionless systems, Ziso = 2d. With friction, Ziso would be lower and depend on the friction coefficient, as fewer contacts are required to achieve force balance.
Potential for New Phases: Friction could introduce new phases or alter the existing ones. For instance, a state with strong force chains stabilized by friction might emerge, potentially exhibiting different rheological properties.
Impact on Fragile States:

Enhanced Stability: Fragile states, characterized by low potential energy but mechanical instability, could become more stable with friction. The frictional forces could help maintain the percolating force network, preventing its collapse.
Dependence on Friction Coefficient: The stability of fragile states would likely depend on the magnitude of the friction coefficient. Higher friction would provide stronger resistance to rearrangements, potentially leading to a wider range of stable fragile states.
Modified Percolation Properties: The percolation properties of the force network, crucial for distinguishing fragile and jammed states, would be altered. Friction could facilitate percolation at lower coordination numbers, blurring the distinction between fragile and jammed states based solely on percolation.
Overall, incorporating friction adds complexity to the jamming transition, potentially leading to a richer phenomenology with new phases and modified critical behavior. The stability of fragile states would be enhanced, with the degree of stabilization depending on the friction coefficient.

Could the observed first-order transition with quenched disorder be an artifact of the quasi-static shear protocol, and would a different dynamic protocol lead to different conclusions?

While the study convincingly demonstrates a first-order transition with quenched disorder under cyclic quasi-static shear (CAQS), it's crucial to consider whether this observation is protocol-dependent.
Arguments against it being an artifact:

Erasing Memory Effects: The study shows that CAQS eliminates the memory of the initial jamming density, suggesting that the observed behavior is not simply a consequence of the initial configuration.
Consistency with J-Point Density: The jamming density obtained from CAQS aligns with the J-point density, the minimum jamming density achievable through rapid quenching. This suggests a degree of robustness in the observed transition point.
Potential influence of different protocols:

Finite Shear Rate Effects: The quasi-static limit assumes infinitely slow shear rates, which is practically unattainable. Finite shear rates could introduce non-equilibrium effects, potentially influencing the observed transition behavior.
Alternative Driving Forces: Using different dynamic protocols, such as oscillatory shear or constant shear rate, could alter the system's response and potentially lead to different conclusions about the nature of the transition. For instance, oscillatory shear might reveal a frequency-dependent transition point or critical exponents.
Influence of Strain Amplitude: The study primarily focuses on a specific strain amplitude (γmax = 0.7). Exploring a wider range of strain amplitudes could reveal whether the first-order nature of the transition persists or if other dynamic regimes emerge.
In conclusion, while the study provides strong evidence for a first-order transition with quenched disorder under CAQS, further investigations using different dynamic protocols are essential to confirm the universality of this finding. Exploring finite shear rate effects, alternative driving forces, and varying strain amplitudes will provide a more comprehensive understanding of the jamming transition.

How can the insights gained from studying the jamming transition in amorphous materials be applied to understand and control other physical phenomena exhibiting similar phase transition behavior, such as the glass transition or the onset of plasticity in solids?

The insights from studying the jamming transition in amorphous materials offer valuable analogies and potential tools for understanding and controlling other complex phenomena exhibiting phase transition-like behavior:
Glass Transition:

Understanding Structural Arrest: Both jamming and the glass transition involve a dramatic slowing down of dynamics and a transition to a disordered, rigid state. Insights from jamming, particularly regarding the role of disorder, frustration, and diverging length scales, could provide new perspectives on the structural arrest in supercooled liquids.
Predicting Glass-Forming Ability: The connection between jamming and the Gardner phase, characterized by a marginal free energy landscape, might offer clues for predicting the glass-forming ability of different materials based on their potential energy landscapes.
Controlling Dynamics through Packing: Understanding how particle shape and interactions influence the jamming transition could inspire strategies for tuning the packing efficiency and dynamics of glass-forming liquids, potentially leading to the development of new glassy materials with tailored properties.
Onset of Plasticity in Solids:

Predicting Yield Stress: The jamming transition provides a framework for understanding the emergence of rigidity in disordered systems. This could be applied to predict the yield stress of amorphous solids, which is crucial for structural materials.
Designing Tougher Materials: Insights into the role of disorder and heterogeneity in jamming could guide the design of amorphous materials with enhanced toughness and ductility. For example, introducing controlled disorder could hinder the propagation of shear bands, leading to improved mechanical properties.
Controlling Shear Banding: The study's findings on the anisotropy of fragile states and their percolation properties could shed light on the mechanisms of shear banding, a common failure mode in amorphous solids. Understanding these mechanisms could lead to strategies for controlling or suppressing shear banding.
Beyond these specific examples, the jamming transition provides a general framework for understanding the emergence of rigidity and collective behavior in disordered systems. This framework can be applied to a wide range of phenomena, including granular materials, foams, emulsions, and even biological systems like tissues and cells.