Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Microscopic structural origin of slow dynamics in glass-forming liquids

Nature Materials volume 24, pages 268–277 (2025)Cite this article

Subjects

Abstract

Supercooled liquids display sluggish dynamics, often attributed to their structural characteristics, yet the underlying mechanism remains elusive. Here we conduct numerical investigations into the structure–dynamics relationship in model glass-forming liquids, with a specific focus on an elementary particle rearrangement mode known as the ‘T1 process’. We discover that the ability of a T1 process to preserve glassy structural order before and after is pivotal towards determining a liquid’s fragility—whether it exhibits super-Arrhenius-like or Arrhenius-like behaviour. If a T1 process disrupts local structural order, it must occur independently without cooperativity, resulting in Arrhenius-like behaviour. By contrast, if it can maintain order, it sequentially propagates from disordered peripheries to the middle of high-structural-order regions, leading to cooperativity and super-Arrhenius-like behaviour. Our study establishes a microscopic link between liquid-structure ordering, dynamic cooperativity and super-Arrhenius-like dynamics, extending the understanding of the structure–dynamics relationships in supercooled liquids.

Access through your institution
Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Fundamental properties of the new 2D model systems.
Fig. 2: Structural ordering and dynamic heterogeneity of the 2D models.
Fig. 3: Characterization of defects in liquids I and II.
Fig. 4: T1-type particle motion and underlying structural order in three 2D liquids.
Fig. 5: Dynamics and T1 processes of PHD at T = 0.00225.

Similar content being viewed by others

Data availability

All data that support the findings of this study are available in the Article and the Supplementary Information.

Code availability

All codes used for simulation and analysis are available from the corresponding author upon request.

References

  1. Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995).

    CAS  PubMed  Google Scholar 

  2. Angell, C. A., Ngai, K. L., McKenna, G. B., McMillan, P. F. & Martin, S. W. Relaxation in glassforming liquids and amorphous solids. J. Appl. Phys. 88, 3113–3157 (2000).

    CAS  Google Scholar 

  3. Ediger, M. D. Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem. 51, 99–128 (2000).

    CAS  PubMed  Google Scholar 

  4. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    CAS  PubMed  Google Scholar 

  5. Dyre, J. C. Colloquium: the glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys. 78, 953–972 (2006).

    CAS  Google Scholar 

  6. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587–645 (2011).

    CAS  Google Scholar 

  7. Tanaka, H. Bond orientational order in liquids: towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization. Eur. Phys. J. E 35, 113 (2012).

    PubMed  Google Scholar 

  8. Royall, C. P. & Williams, S. R. The role of local structure in dynamical arrest. Phys. Rep. 560, 1–75 (2015).

    CAS  Google Scholar 

  9. Hurley, M. M. & Harrowell, P. Kinetic structure of a two-dimensional liquid. Phys. Rev. E 52, 1694–1698 (1995).

    CAS  Google Scholar 

  10. Widmer-Cooper, A. & Harrowell, P. Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities. Phys. Rev. Lett. 96, 185701 (2006).

    PubMed  Google Scholar 

  11. Shintani, H. & Tanaka, H. Frustration on the way to crystallization in glass. Nat. Phys. 2, 200–206 (2006).

    CAS  Google Scholar 

  12. Coslovich, D. & Pastore, G. Understanding fragility in supercooled Lennard-Jones mixtures. I. Locally preferred structures. J. Chem. Phys. 127, 124504 (2007).

    CAS  PubMed  Google Scholar 

  13. Tanaka, H., Kawasaki, T., Shintani, H. & Watanabe, K. Critical-like behaviour of glass-forming liquids. Nat. Mater. 9, 324–331 (2010).

    CAS  PubMed  Google Scholar 

  14. Xia, C. et al. The structural origin of the hard-sphere glass transition in granular packing. Nat. Commun. 6, 8409 (2015).

    CAS  PubMed  Google Scholar 

  15. Tong, H. & Tanaka, H. Revealing hidden structural order controlling both fast and slow glassy dynamics in supercooled liquids. Phys. Rev. X 8, 011041 (2018).

    CAS  Google Scholar 

  16. Tong, H. & Tanaka, H. Structural order as a genuine control parameter of dynamics in simple glass formers. Nat. Commun. 10, 5596 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. Tong, H. & Tanaka, H. Role of attractive interactions in structure ordering and dynamics of glass-forming liquids. Phys. Rev. Lett. 124, 225501 (2020).

    CAS  PubMed  Google Scholar 

  18. Zheng, Z., Ni, R., Wang, Y. & Han, Y. Translational and rotational critical-like behaviors in the glass transition of colloidal ellipsoid monolayers. Sci. Adv. 7, eabd1958 (2021).

    PubMed  PubMed Central  Google Scholar 

  19. Singh, N., Zhang, Z., Sood, A. K., Kob, W. & Ganapathy, R. Intermediate-range order governs dynamics in dense colloidal liquids. Proc. Natl Acad. Sci. USA 120, e2300923120 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Chandler, D. & Garrahan, J. P. Dynamics on the way to forming glass: bubbles in space-time. Annu. Rev. Phys. Chem. 61, 191–217 (2010).

    CAS  PubMed  Google Scholar 

  21. Kob, W., Donati, C., Plimpton, S. J., Poole, P. H. & Glotzer, S. C. Dynamical heterogeneities in a supercooled Lennard-Jones liquid. Phys. Rev. Lett. 79, 2827–2830 (1997).

    CAS  Google Scholar 

  22. Yamamoto, R. & Onuki, A. Dynamics of highly supercooled liquids: heterogeneity, rheology, and diffusion. Phys. Rev. E 58, 3515–3529 (1998).

    CAS  Google Scholar 

  23. Sherrington, D., Davison, L., Buhot, A. & Garrahan, J. P. Glassy behaviour in simple kinetically constrained models: topological networks, lattice analogues and annihilation-diffusion. J. Phys. Condens. Matter 14, 1673 (2002).

    CAS  Google Scholar 

  24. Langer, J. S. Dynamics and thermodynamics of the glass transition. Phys. Rev. E 73, 041504 (2006).

    CAS  Google Scholar 

  25. Eckmann, J.-P. & Procaccia, I. Ergodicity and slowing down in glass-forming systems with soft potentials: no finite-temperature singularities. Phys. Rev. E 78, 011503 (2008).

    Google Scholar 

  26. Bouchbinder, E. & Langer, J. S. Shear-transformation-zone theory of linear glassy dynamics. Phys. Rev. E 83, 061503 (2011).

    Google Scholar 

  27. Zhou, Y. & Milner, S. T. T1 process and dynamics in glass-forming hard-sphere liquids. Soft Matter 11, 2700–2705 (2015).

    CAS  PubMed  Google Scholar 

  28. Socolar, J. E. S., Lubensky, T. C. & Steinhardt, P. J. Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986).

    CAS  Google Scholar 

  29. Adam, G. & Gibbs, J. H. On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965).

    CAS  Google Scholar 

  30. Russo, J., Romano, F. & Tanaka, H. Glass forming ability in systems with competing orderings. Phys. Rev. X 8, 021040 (2018).

    CAS  Google Scholar 

  31. Donati, C. et al. Stringlike cooperative motion in a supercooled liquid. Phys. Rev. Lett. 80, 2338–2341 (1998).

    CAS  Google Scholar 

  32. Bouchaud, J.-P. & Biroli, G. On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 121, 7347–7354 (2004).

    CAS  PubMed  Google Scholar 

  33. Betancourt, B. A. P., Hanakata, P. Z., Starr, F. W. & Douglas, J. F. Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials. Proc. Natl Acad. Sci. USA 112, 2966–2971 (2015).

    Google Scholar 

  34. Kob, W. & Andersen, H. C. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture. II. Intermediate scattering function and dynamic susceptibility. Phys. Rev. E 52, 4134–4153 (1995).

    CAS  Google Scholar 

  35. Böhmer, R., Ngai, K. L., Angell, C. A. & Plazek, D. J. Nonexponential relaxations in strong and fragile glass formers. J. Chem. Phys. 99, 4201–4209 (1993).

    Google Scholar 

  36. Onuki, A. Phase Transition Dynamics (Cambridge Univ. Press, 2002).

  37. Lačević, N., Starr, F. W., Schrøder, T. B. & Glotzer, S. C. Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function. J. Chem. Phys. 119, 7372–7387 (2003).

    Google Scholar 

  38. Mosayebi, M., Del Gado, E., Ilg, P. & Öttinger, H. C. Probing a critical length scale at the glass transition. Phys. Rev. Lett. 104, 205704 (2010).

    PubMed  Google Scholar 

  39. Gilman, J. J. Dislocation mobility in crystals. J. Appl. Phys. 36, 3195–3206 (1965).

    CAS  Google Scholar 

  40. Galwey, A. K. & Brown, M. E. A theoretical justification for the application of the Arrhenius equation to kinetics of solid state reactions (mainly ionic crystals). Proc. Royal Soc. Lond. A 450, 501–512 (1995).

    CAS  Google Scholar 

  41. Langer, J. S. Ising model of a glass transition. Phys. Rev. E 88, 012122 (2013).

    CAS  Google Scholar 

  42. Tanaka, H., Tong, H., Shi, R. & Russo, J. Revealing key structural features hidden in liquids and glasses. Nat. Rev. Phys. 1, 333–348 (2019).

    Google Scholar 

  43. Horbach, J., Kob, W. & Binder, K. Molecular dynamics simulation of the dynamics of supercooled silica. Philos. Mag. B 77, 297–303 (1998).

    CAS  Google Scholar 

  44. Horbach, J. & Kob, W. Static and dynamic properties of a viscous silica melt. Phys. Rev. B 60, 3169–3181 (1999).

    CAS  Google Scholar 

  45. Shi, R. & Tanaka, H. Impact of local symmetry breaking on the physical properties of tetrahedral liquids. Proc. Natl Acad. Sci. USA 115, 1980–1985 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  46. Zargar, R., Nienhuis, B., Schall, P. & Bonn, D. Direct measurement of the free energy of aging hard sphere colloidal glasses. Phys. Rev. Lett. 110, 258301 (2013).

    PubMed  Google Scholar 

  47. Mei, B., Zhuang, B., Lu, Y., An, L. & Wang, Z.-G. Local-average free volume correlates with dynamics in glass formers. J. Phys. Chem. Lett. 13, 3957–3964 (2022).

    CAS  PubMed  Google Scholar 

  48. Scalliet, C., Guiselin, B. & Berthier, L. Thirty milliseconds in the life of a supercooled liquid. Phys. Rev. X 12, 041028 (2022).

    CAS  Google Scholar 

  49. Tanaka, H. Roles of liquid structural ordering in glass transition, crystallization, and water’s anomalies. J. NonCryst. Solids X 13, 100076 (2022).

    CAS  Google Scholar 

  50. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    CAS  Google Scholar 

  51. Flenner, E. & Szamel, G. Fundamental differences between glassy dynamics in two and three dimensions. Nat. Commun. 6, 7392 (2015).

    CAS  PubMed  Google Scholar 

  52. Shiba, H., Yamada, Y., Kawasaki, T. & Kim, K. Unveiling dimensionality dependence of glassy dynamics: 2D infinite fluctuation eclipses inherent structural relaxation. Phys. Rev. Lett. 117, 245701 (2016).

    PubMed  Google Scholar 

  53. Illing, B. et al. Mermin–Wagner fluctuations in 2D amorphous solids. Proc. Natl Acad. Sci. USA 114, 1856–1861 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  54. Vivek, S., Kelleher, C. P., Chaikin, P. M. & Weeks, E. R. Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions. Proc. Natl Acad. Sci. USA 114, 1850–1855 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

This work was partially supported by Specially Promoted Research (JP25000002 and JP20H05619) and Scientific Research (A) (JP18H03675) from the Japan Society of the Promotion of Science (JSPS).

Author information

Author notes

  1. These authors contributed equally: Seiichiro Ishino, Yuan-Chao Hu.

Authors and Affiliations

  1. Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Seiichiro Ishino, Yuan-Chao Hu & Hajime Tanaka

  2. Songshan Lake Materials Laboratory, Dongguan, China

    Yuan-Chao Hu

  3. Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan

    Hajime Tanaka

Authors
  1. Seiichiro Ishino
    View author publications

    Search author on:PubMed Google Scholar

  2. Yuan-Chao Hu
    View author publications

    Search author on:PubMed Google Scholar

  3. Hajime Tanaka
    View author publications

    Search author on:PubMed Google Scholar

Contributions

H.T. conceived and supervised the project; S.I. and Y.-C.H. performed numerical simulations. S.I., Y.-C.H. and H.T. discussed the results and wrote the manuscript.

Corresponding author

Correspondence to Hajime Tanaka.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Yujie Wang, Lothar Wondraczek and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 An example of structural characterisation of the 2D nonadditive systems.

A zero-temperature diffraction pattern. The scattering pattern for (η, cB) = (0.65, 0.3) and Q = 10−5.5 reveals a distinct 12-fold symmetry pattern characteristic of a dodecagonal quasi-crystal.

Extended Data Fig. 2 Temperature dependence of the self-intermediate scattering functions for the three liquids.

a, Liquid I. b, Liquid II. c, PHD. See Methods for details on calculating the self-intermediate scattering function Fs(q, t).

Extended Data Fig. 3 Comparison of structure and dynamics obtained from the isoconfigurational ensemble for the ‘fragile’ PHD (a-d, T=0.0024) and the ‘strong’ liquid II (e-h, T=0.018).

a, The spatial distribution of the local structural order parameter \({\Psi }_{6}^{c}\) coarse-grained over its spatial correlation length ξ6 (see the colour bar) (see refs. 15,16 for the meaning of the coarse-graining). b-d, Cage-relative atomic displacements (see the colour bar) during 1τα, 5τα, and 10τα averaged from 300 independent runs starting from the same initial structure as in a.e, The spatial distribution of the local structural order parameter Ψ8 (see the colour bar). f-h, Cage-relative atomic displacements (see the colour bar) during 1τα, 5τα, and 10τα averaged from 300 independent runs starting from the same initial structure as in e. Common features in these two systems include the correspondence between dynamical heterogeneity and the structural order parameter field, as well as their homogenisation as the ordered region gradually becomes disordered over time. After a long time, every atom will have completed structural relaxation with large displacements. We can see that dynamic heterogeneity is much longer-lived for liquid II than for PHD.

Extended Data Fig. 4 The spatial decay of the correlation of structural order parameters.

a-c, The temperature dependences of g12(r)/g(r), g8(r)/g(r), and g6(r)/g(r) for liquid I, liquid II, and PHD, respectively. The dashed lines represent fits to the OZ functions, from which we determine the structural correlation length ξ12, ξ8, and ξ6. We can see the increase of the structural correlation length upon cooling for the three liquids. The correlation lengths estimated in this manner are presented in Fig. 2f-h.

Extended Data Fig. 5 Temperature dependence of dynamic heterogeneities.

a-c, The temperature dependences of χ4 (t) of liquid I, liquid II, and PHD, respectively. In all systems, χ4 (t) exhibits a rapid increase with decreasing temperature. This behaviour is noticeable even for liquid II, which is a strong liquid. It is uncommon to observe such pronounced dynamic heterogeneity in strong liquids. Notably, the peak magnitudes of χ4 (t) of liquid II are smaller than those for liquid I and PHD. This trend aligns with the steep decrease in the stretching exponent, β, for liquid II upon cooling (see Fig. 1f in the main text). The underlying reason for this seemingly counterintuitive result is explained in the main text. d-f, The temperature changes of the q-dependence of S4(τ4) for liquid I, liquid II, and PHD, respectively. The solid curves represent fits of the Ornstein-Zernike correlation function to the data, allowing us to determine ξdyn.

Extended Data Fig. 6 The non-Gaussian nature of particle diffusion.

a-c, The temperature dependences of the non-Gaussian parameter α2 (t) for liquid I, liquid II, and PHD, respectively. The peak of α2 (t) shows a sharp increase with decreasing temperature in all three systems, indicating the enhancement of dynamic heterogeneity.

Extended Data Fig. 7 Atomic-scale mechanism of structural relaxation for a locally favoured structure in fragile liquids (liquid I and PHD).

a-c, Liquid I. a, Depiction of an LFS motif comprised of 8 red particles exhibiting a pentagonal shape (marked by orange lines). Each particle is labelled with numbers 1-8 to monitor their movements. b, Illustration of the LFS transformation into an intermediate disordered state by two T1 processes (yellow triangles). Each T1 process involves four particles breaking old bonds and creating new ones. c, Formation of a new LFS (orange pentagon) through two successive T1 processes (yellow triangles). The centre of the new LFS retains 6 old neighbours and gains a new neighbour, resulting in the transformation from the initial loose pentagon-shaped arrangement to a new, tight-packed LFS. Therefore, the old LFS shown in panel a undergoes a rotation to transform into the new LFS through this particle rearrangement process. B particles are shown in blue and large, while A particles are depicted in green for better visualisation. d-f, PHD. d, Depiction of an LFS motif with hexatic ordering. Each particle is labelled with numbers 1–9 to track their movements. e, Occurrence of a T1 process among atoms 1–2–3–7 from panel d, creating an intermediate disordered state. f, Another T1 process among atoms 1–4–8–9 from panel e. The central atom (red) escapes from its initial cage formed by atoms 2–3–4–5–6–7 (see panel d) while maintaining the order of 4–5–7–3–8–9 during sequential T1 events. In this polydisperse system, atoms are represented as equal-sized for simplicity in visualisation.

Extended Data Fig. 8 Phason-flip-like particle motion observed in liquid I.

a, Visualization of particle motion in liquid I at T=0.041 over a time interval Δt = 1.2. Filled red and black circles represent A and B particles at t=0, whereas open red and black circles represent their positions at t=1.2. The particle motion of 6 particles is depicted by a red-shaded combined square and triangle at t=0 and a white-shaded one at t=1.2. This particle motion is analogous to the phason-flip motion observed in a 12-fold quasi-crystal. b, Decomposition of the phason-flip-like motion (top row) into two T1 processes (two bottom rows). Three particles mainly move in the process, as indicated by arrows, leading to the occurrence of two T1 processes. In the right images, newly formed and broken bonds are represented by solid and broken lines, respectively.

Extended Data Fig. 9 Comparison of the self-intermediate scattering functions Fs(q, t) between absolute and cage-relative particle motion at T=0.00225 for PHD.

The time when Fs(q, t) = 1/e is defined as \({\tau }_{ \alpha }^{{\rm{abs}}}(\approx 440)\) and τα (≈ 104) for absolute and cage-relative motion, respectively. Therefore, at this temperature, \({\tau }_{ \alpha }\cong 23{\tau }_{\rm \alpha }^{{\rm{abs}}}\). The former is influenced by Mermin-Wagner-type fluctuations, whereas the latter is free from such effects.

Supplementary information

Supplementary Information

Supplementary Notes 1 and 2, Figs. 1 and 2 and references.

Reporting Summary

Supplementary Video 1

Dynamics and T1 processes in 2D PHD supercooled liquid.

Supplementary Video 2

Dynamics and T1 processes in 3D PHS supercooled liquid.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ishino, S., Hu, YC. & Tanaka, H. Microscopic structural origin of slow dynamics in glass-forming liquids. Nat. Mater. 24, 268–277 (2025). https://doi.org/10.1038/s41563-024-02068-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41563-024-02068-8

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing