[Paper Review] Local vs. Cooperative: Unraveling Glass Transition Mechanisms with SEER

Massimo Pica Ciamarra, Wencheng Ji+1 more|arXiv (Cornell University)|Feb 10, 2023

Material Dynamics and Properties4 citations

TL;DR

This paper introduces SEER, a novel algorithm to systematically extract local excitations and their energy barriers from supercooled liquid configurations. It finds that local energy barriers—shifted to higher values upon cooling—quantitatively control relaxation dynamics up to millisecond timescales, challenging cooperative theories of the glass transition and suggesting local barriers dominate fragility.

ABSTRACT

Which phenomenon slows down the dynamics in super-cooled liquids and turns them into glasses is a long-standing question of condensed-matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or `excitations' govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, SEER, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a novel measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.

Motivation & Objective

• To resolve the long-standing debate on whether cooperative dynamics or local energy barriers govern the slowdown near the glass transition.
• To develop a systematic method for identifying and quantifying local excitations in supercooled liquids from equilibrium configurations.
• To test whether the temperature dependence of local energy barriers alone can explain observed relaxation dynamics up to millisecond timescales.
• To challenge prevailing cooperative theories (e.g., Adam-Gibbs, KCMs) by quantitatively comparing predictions from local barrier models against simulation data.

Proposed method

• SEER systematically identifies local excitations by minimizing energy along paths from a given configuration, using the nudged elastic band method to locate minimum energy pathways.
• For each identified excitation, SEER computes its energy barrier by determining the smallest stiffness parameter $ k_e $ that suppresses the excitation, ensuring stability and convergence.
• The algorithm uses thermal cycles with varying waiting times $ t_w $ and ensemble averaging over 50 independent runs to ensure statistical robustness and convergence of the excitation catalogue.
• Duplicate excitations are removed by applying a distance threshold $ d_{ij} $, ensuring only distinct, well-separated excitations are retained in the final catalogue.
• The energy shift $ riangle E $ of inherent structures is estimated by quenching equilibrium configurations to low temperature and analyzing the gap between the initial and final energy states.
• Time-temperature superposition is applied to overlap correlation functions, confirming stretched exponential decay with $ eta acksimeq 0.52 $, enabling relaxation time estimation at low temperatures.

Figure 1: a Temperature dependence of the relaxation time $\tau$ estimated from the decay of the overlap function in our poly-disperse (see Sec. III ). It is customary to define the onset temperature $T_{\rm on}$ as the temperature below which the energy of inherent structures starts to decrease. $T

Experimental results

Research questions

• RQ1 Do local energy barriers, rather than growing cooperative length scales, control the slowing down of dynamics near the glass transition?
• RQ2 Can the temperature dependence of local excitation energy barriers quantitatively predict relaxation times up to millisecond scales in equilibrated supercooled liquids?
• RQ3 How robust is the SEER algorithm in extracting distinct excitations across different thermal histories and system sizes?
• RQ4 To what extent do cooperative effects contribute to the observed fragility, given the dominance of local barriers in the dynamics?

Key findings

• The excitation density of states shifts to higher energy upon cooling, directly linking increasing energy barriers to the slowing of relaxation dynamics.
• The predicted relaxation times based solely on local barrier energy shifts show quantitative agreement with simulation data up to millisecond timescales.
• The number of discovered excitations converges with increasing $ N_E $, and is insensitive to the waiting time $ t_w $, confirming algorithmic stability and robustness.
• Outlier configurations with anomalously high $ riangle E $ at high temperatures are eliminated by avoiding instantaneous quenching, improving consistency across samples.
• The use of elementary excitations (single maximum) yields more reliable gap energy estimates than complex excitations, which are prone to fortuitous combinations.
• Time-temperature superposition confirms stretched exponential decay of overlap functions with $ eta acksimeq 0.52 $, enabling reliable relaxation time estimation at low temperatures.

Figure 2: Schematic illustration of SEER’s working principle. a The algorithm suppresses a discovered excitation by transforming it into a saddle bifurcation; b in real space, it corresponds to adding restoring forces opposite to displacements along the suppressed excitations.