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Autonomously revealing hidden local structures in supercooled liquids

Emanuele Boattini, Susana Marín-Aguilar, Saheli Mitra, Giuseppe Foffi, Frank Smallenburg, Laura Filion

arXiv:2003.00586v1cond-mat.soft

TL;DR

The paper asks whether purely structural information can identify local structures connected to slow dynamics, without relying on dynamical information for their identification. It applies unsupervised machine learning to local structure in three glass formers and finds strong correlations with dynamical heterogeneity, while the structures linked to slow particles disappear away from the glass transition.

  • Problem

    It remains open whether purely structural information can identify structures linked to slow dynamics, since prior searches have often used dynamical information.

    Source: p. 1

  • Method

    An autoencoder-based unsupervised method uses local bond order parameters to identify structural heterogeneities from local structure.

    Source: pp. 1, 5

  • Results

    The identified structural heterogeneities strongly correlate with dynamical heterogeneity in all three studied glass formers.

    Source: p. 5

  • Takeaways & Limitations

    The structural characteristics linked to slow particles disappear as the systems move away from the glass transition.

    Source: pp. 2, 4

Abstract

from arXiv · show

Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids and glasses. The conundrum: close to the glass transition, the dynamics slow down dramatically and become heterogeneous while the structure appears largely unperturbed. Largely unperturbed, however, is not the same as unperturbed, and many studies have attempted to identify "slow" local structures by exploiting dynamical information. Nonetheless, the question remains open: is the key to the slow dynamics imprinted in purely structural information? And if so, is there a way to determine the relevant structures without any dynamical information? Here, we use a newly developed unsupervised machine learning (UML) algorithm to identify structural heterogeneities in three archetypical glass formers. In each system, the UML approach autonomously designs an order parameter based purely on structural variation within a single snapshot. Impressively, this order parameter strongly correlates with the dynamical heterogeneity. Moreover, the structural characteristics linked to slow particles disappear as we move away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.

Models

The study compares binary hard spheres with the Wahnström and Kob-Andersen Lennard-Jones mixtures. The mixtures differ in composition and interaction parameters.

Models

  • The three glass formers are binary hard spheres, Wahnström, and Kob-Andersen; the latter two are Lennard-Jones mixtures.Source: Models · p. 5
  • The hard-sphere mixture contains 30% large A particles and 70% small B particles, with σB/σA = 0.85.Source: Models · p. 5
  • Wahnström is equimolar, with identical pair interaction strengths and larger B particles; its truncated-and-shifted Lennard-Jones potential is purely repulsive.The size parameters are σBB = 1.2σAA and σAB = 1.1σAA.Source: Models · p. 5
  • Kob-Andersen contains 80% large A and 20% small B particles, with non-additive parameters and an attractive part retained in its truncated-and-shifted potential.The cutoff is rc,ij = 2.5σij; σBB = 0.88σAA, σAB = 0.8σAA, ϵBB = 0.5ϵAA, and ϵAB = 1.5ϵAA.Source: Models · p. 5
  • For both Lennard-Jones mixtures, reduced density is defined using ρσAA^3 and reduced temperature as T* = kBT/ϵAA.Source: Models · p. 5

Simulations

The authors simulate all models in the canonical ensemble and estimate particle mobility from repeated runs begun from the same configuration. They obtain relaxation times from intermediate scattering functions.

Simulations

  • All models are simulated in the canonical ensemble, using event-driven dynamics for hard spheres and LAMMPS for the two Lennard-Jones systems.Source: Simulations · p. 5
  • Dynamic propensity is the isoconfigurational average of each particle’s absolute displacement, measured over at least 32 runs with randomized velocities from the same initial configuration.The average is taken over independent runs.Source: Simulations · p. 5
  • Relaxation times are obtained from the self-intermediate scattering function for Wahnström and Kob-Andersen and the total intermediate scattering function for hard spheres.The long-time decay is fit with a stretched exponential; the relaxation time τα is a fit parameter.Source: Simulations · p. 5

Local environment description

Each particle’s local environment is represented using averaged bond order parameters. The resulting eight-component description uses neighbor sets defined by model-specific criteria.

Local environment description

  • Local environments are characterized using an averaged version of Steinhardt bond order parameters.Source: Local environment description · pp. 5–6
  • The averaged bond order parameters differ from Lechner and Dellago’s approach, which averages the non-rotational-invariant qlm quantities before constructing rotationally invariant values.Source: Local environment description · p. 6
  • The local description is an eight-dimensional vector composed of the averaged bond order parameters for l from 1 to 8.Source: Local environment description · p. 6
  • For hard spheres and Wahnström, SANN assigns each particle an individual cutoff based on its local environment; the authors enforce symmetric neighbor relations by removing one-sided neighbors.For Kob-Andersen, a fixed cutoff gives better results.Source: Local environment description · p. 6

Unsupervised machine learning

The paper uses the UML method previously outlined in Ref.; a detailed account is provided in the Supplemental Information.

Unsupervised machine learning

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