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Unified percolation scenario for the α and β processes in simple glass formers

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Abstract

Given the vast differences in interaction details, describing the dynamics of structurally disordered materials in a unified theoretical framework presents a fundamental challenge to condensed-matter physics and materials science. Here we numerically investigate a double-percolation scenario for the two most important relaxation processes of supercooled liquids and glasses, the so-called α and β relaxations. For several simple glass formers, we find that when monitoring the dynamic shear modulus as temperature is lowered from the liquid state, percolation of immobile particles takes place at the temperature locating the α process. Mirroring this, upon continued cooling into the glass state, the mobile-particle percolation transition pinpoints a β process whenever the latter is well separated from the main (α) process. For two-dimensional systems under the same conditions, percolation of mobile and immobile particles occurs nearly simultaneously, and no β relaxation can be identified. Our findings suggest that a general description of glassy dynamics should be based on a percolation perspective.

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Fig. 1: Main concepts.
Fig. 2: Double-percolation studies.
Fig. 3: Double-percolation studies of systems with close percolation temperatures.
Fig. 4: The ratio between mobile and immobile percolation temperatures determines the β process manifestation.
Fig. 5: Double-percolation studies of 2D models.
Fig. 6: Temperature dependence of the α and β average relaxation times and of the immobile- and mobile-particle percolation times.

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Data availability

All of the data used to generate Figs. 16 are available via Zenodo at https://doi.org/10.5281/zenodo.13925660 (ref. 96).

Code availability

The simulation package LAMMPS (https://www.lammps.org) was used for all molecular dynamics simulations. The code and scripts of the analysis are available via Zenodo at https://doi.org/10.5281/zenodo.13925660 (ref. 96).

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Acknowledgements

The computational work was carried out on the public computing service platform provided by the Network and Computing Center of HUST. We thank the National Natural Science Foundation of China for support (grant no. 52071147 (H.-B.Y.)). This work was also supported by the VILLUM Foundation’s Matter grant no. VIL16515 (J.C.D.).

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H.-B.Y. and J.C.D. devised the project. L.G. and H.-B.Y. performed the simulations with input from T.B.S. and J.C.D. All authors wrote and revised the manuscript.

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Correspondence to Hai-Bin Yu or Jeppe C. Dyre.

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Gao, L., Yu, HB., Schrøder, T.B. et al. Unified percolation scenario for the α and β processes in simple glass formers. Nat. Phys. 21, 471–479 (2025). https://doi.org/10.1038/s41567-024-02762-z

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