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Distinct elastic properties and their origins in glasses and gels

Nature Physics (2024)Cite this article

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Abstract

Glasses and gels, common amorphous solids with diverse applications, share intriguing similarities, including rigidity without translational order and dynamic slowing during ageing. However, their various underlying differences have not yet been explained. Here, through simulations, we elucidate distinct elastic properties related to temperature, observation times and ageing in glasses and gels, uncovering the underlying mechanisms. Configurational constraints, characterized by vibrational mean-squared displacements, similarly impact shear and bulk moduli in gels, but uniquely affect the shear modulus in glasses. As glasses age, a persistent trend of stiffening emerges, in contrast to gels, which initially stiffen and subsequently soften. We attribute these differences to mechanisms minimizing free energy: structural ordering in glasses and interface reduction in gels. Our findings not only reveal distinct behaviours but also shed light on the origin and evolution of elasticity in non-equilibrium disordered solids, with implications for amorphous material application and design.

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Fig. 1: Ageing dynamics and observation-time-dependent elasticity in glasses and gels.
Fig. 2: Age-dependent elasticity in glasses and gels.
Fig. 3: Role of inherent elasticity and MSD on thermal elasticity.
Fig. 4: Age-dependent potential energy and structure in glasses and gels.
Fig. 5: Illustration of the origin of elasticity and distinct ageing mechanisms in glasses and gels.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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The codes used in this study are available from the corresponding author upon reasonable request.

References

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

    Article  ADS  Google Scholar 

  2. Wang, W. H. The elastic properties, elastic models and elastic perspectives of metallic glasses. Prog. Mater. Sci. 57, 487–656 (2012).

    Article  Google Scholar 

  3. Zaccarelli, E. Colloidal gels: equilibrium and non-equilibrium routes. J. Phys. Condens. Matter 19, 323101 (2007).

    Article  Google Scholar 

  4. Royall, C. P., Faers, M. A., Fussell, S. L. & Hallett, J. E. Real space analysis of colloidal gels: triumphs, challenges and future directions. J. Phys. Condens. Matter 33, 453002 (2021).

    Article  ADS  Google Scholar 

  5. Baus, M. Statistical mechanical theories of freezing: an overview. J. Stat. Phys. 48, 1129–1146 (1987).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  7. Bonn, D., Denn, M. M., Berthier, L., Divoux, T. & Manneville, S. Yield stress materials in soft condensed matter. Rev. Mod. Phys. 89, 035005 (2017).

    Article  ADS  Google Scholar 

  8. Lu, P. J. et al. Gelation of particles with short-range attraction. Nature 453, 499–503 (2008).

    Article  ADS  Google Scholar 

  9. Zia, R. N., Landrum, B. J. & Russel, W. B. A micro-mechanical study of coarsening and rheology of colloidal gels: cage building, cage hopping, and Smoluchowski’s ratchet. J. Rheol. 58, 1121–1157 (2014).

    Article  ADS  Google Scholar 

  10. Testard, V., Berthier, L. & Kob, W. Influence of the glass transition on the liquid-gas spinodal decomposition. Phys. Rev. Lett. 106, 125702 (2011).

    Article  ADS  Google Scholar 

  11. Testard, V., Berthier, L. & Kob, W. Intermittent dynamics and logarithmic domain growth during the spinodal decomposition of a glass-forming liquid. J. Chem. Phys. 140, 164502 (2014).

    Article  ADS  Google Scholar 

  12. Whitaker, K. A. et al. Colloidal gel elasticity arises from the packing of locally glassy clusters. Nat. Commun. 10, 2237 (2019).

    Article  ADS  Google Scholar 

  13. Tsurusawa, H., Leocmach, M., Russo, J. & Tanaka, H. Direct link between mechanical stability in gels and percolation of isostatic particles. Sci. Adv. 5, eaav6090 (2019).

    Article  ADS  Google Scholar 

  14. Hsiao Lilian, C., Newman Richmond, S., Glotzer Sharon, C. & Solomon Michael, J. Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels. Proc. Natl Acad. Sci. USA 109, 16029–16034 (2012).

    Article  ADS  Google Scholar 

  15. Patrick Royall, C., Williams, S. R., Ohtsuka, T. & Tanaka, H. Direct observation of a local structural mechanism for dynamic arrest. Nat. Mater. 7, 556–561 (2008).

    Article  ADS  Google Scholar 

  16. Zhang, S. et al. Correlated rigidity percolation and colloidal gels. Phys. Rev. Lett. 123, 058001 (2019).

    Article  ADS  Google Scholar 

  17. Tsurusawa, H. & Tanaka, H. Hierarchical amorphous ordering in colloidal gelation. Nat. Phys. 19, 1171–1177 (2023).

  18. Joshi, Y. M. Dynamics of colloidal glasses and gels. Annu. Rev. Chem. Biomol. Eng. 5, 181–202 (2014).

    Article  Google Scholar 

  19. Ruzicka, B. & Zaccarelli, E. A fresh look at the Laponite phase diagram. Soft Matter 7, 1268–1286 (2011).

    Article  ADS  Google Scholar 

  20. Alexander, S. Amorphous solids: their structure, lattice dynamics and elasticity. Phys. Rep. 296, 65–236 (1998).

    Article  ADS  Google Scholar 

  21. DeGiuli, E. Field theory for amorphous solids. Phys. Rev. Lett. 121, 118001 (2018).

    Article  ADS  Google Scholar 

  22. Lemaître, A. Stress correlations in glasses. J. Chem. Phys. 149, 104107 (2018).

    Article  ADS  Google Scholar 

  23. Nampoothiri, J. N. et al. Emergent elasticity in amorphous solids. Phys. Rev. Lett. 125, 118002 (2020).

    Article  ADS  Google Scholar 

  24. Wang, Y., Wang, Y. & Zhang, J. Connecting shear localization with the long-range correlated polarized stress fields in granular materials. Nat. Commun. 11, 4349 (2020).

    Article  ADS  Google Scholar 

  25. Yoshino, H. & Mézard, M. Emergence of rigidity at the structural glass transition: a first-principles computation. Phys. Rev. Lett. 105, 015504 (2010).

    Article  ADS  Google Scholar 

  26. Yoshino, H. & Zamponi, F. Shear modulus of glasses: results from the full replica-symmetry-breaking solution. Phys. Rev. E 90, 022302 (2014).

    Article  ADS  Google Scholar 

  27. Szamel, G. & Flenner, E. Emergence of long-range correlations and rigidity at the dynamic glass transition. Phys. Rev. Lett. 107, 105505 (2011).

    Article  ADS  Google Scholar 

  28. Parisi, G. & Zamponi, F. Mean-field theory of hard sphere glasses and jamming. Rev. Mod. Phys. 82, 789–845 (2010).

    Article  ADS  Google Scholar 

  29. Yanagishima, T., Russo, J. & Tanaka, H. Common mechanism of thermodynamic and mechanical origin for ageing and crystallization of glasses. Nat. Commun. 8, 15954 (2017).

    Article  ADS  Google Scholar 

  30. Tong, H., Sengupta, S. & Tanaka, H. Emergent solidity of amorphous materials as a consequence of mechanical self-organisation. Nat. Commun. 11, 4863 (2020).

    Article  ADS  Google Scholar 

  31. Ding, J. et al. Universal structural parameter to quantitatively predict metallic glass properties. Nat. Commun. 7, 13733 (2016).

    Article  ADS  Google Scholar 

  32. Saw, S. & Harrowell, P. Rigidity in condensed matter and its origin in configurational constraint. Phys. Rev. Lett. 116, 137801 (2016).

    Article  ADS  Google Scholar 

  33. Greinert, N., Wood, T. & Bartlett, P. Measurement of effective temperatures in an aging colloidal glass. Phys. Rev. Lett. 97, 265702 (2006).

    Article  ADS  Google Scholar 

  34. C. K. Poon, W. et al. Delayed sedimentation of transient gels in colloid-polymer mixtures: dark-field observation, rheology and dynamic light scattering studies. Faraday Discuss. 112, 143–154 (1999).

    Article  ADS  Google Scholar 

  35. Teece, L. J. et al. Gels under stress: The origins of delayed collapse. Colloids Surf. A 458, 126–133 (2014).

    Article  Google Scholar 

  36. Bartlett, P., Teece, L. J. & Faers, M. A. Sudden collapse of a colloidal gel. Phys.Rev. E 85, 021404 (2012).

    Article  ADS  Google Scholar 

  37. Kamp, S. W. & Kilfoil, M. L. Universal behaviour in the mechanical properties of weakly aggregated colloidal particles. Soft Matter 5, 2438–2447 (2009).

    Article  ADS  Google Scholar 

  38. Clarke, A. Gel breakdown in a formulated product via accumulated strain. Soft Matter 17, 7893–7902 (2021).

    Article  ADS  Google Scholar 

  39. Fenton, S. M. et al. Minimal conditions for solidification and thermal processing of colloidal gels. Proc. Natl Acad. Sci. USA 120, e2215922120 (2023).

    Article  Google Scholar 

  40. Bouzid, M. et al. Computing the linear viscoelastic properties of soft gels using an optimally windowed chirp protocol. J. Rheol. 62, 1037–1050 (2018).

    Article  ADS  Google Scholar 

  41. Bantawa, M. et al. The hidden hierarchical nature of soft particulate gels. Nat. Phys. 19, 1178–1184 (2023).

  42. Griffiths, S., Turci, F. & Royall, C. P. Local structure of percolating gels at very low volume fractions. J. Chem. Phys. 146, 014905 (2017).

    Article  ADS  Google Scholar 

  43. Yunker, P., Zhang, Z., Aptowicz, K. B. & Yodh, A. G. Irreversible rearrangements, correlated domains, and local structure in aging glasses. Phys. Rev. Lett. 103, 115701 (2009).

    Article  ADS  Google Scholar 

  44. Tateno, M., Yanagishima, T. & Tanaka, H. Microscopic structural origin behind slowing down of colloidal phase separation approaching gelation. J. Chem. Phys. 156, 084904 (2022).

    Article  ADS  Google Scholar 

  45. Tanaka, H., Nishikawa, Y. & Koyama, T. Network-forming phase separation of colloidal suspensions. J. Phys. Condens. Matter 17, L143 (2005).

  46. Kawasaki, T. & Tanaka, H. Structural evolution in the aging process of supercooled colloidal liquids. Phys. Rev. E 89, 062315 (2014).

    Article  ADS  Google Scholar 

  47. Widmer-Cooper, A. & Harrowell, P. Free volume cannot explain the spatial heterogeneity of Debye–Waller factors in a glass-forming binary alloy. J. Non Cryst. Solids 352, 5098–5102 (2006).

    Article  ADS  Google Scholar 

  48. 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).

    Article  ADS  Google Scholar 

  49. Mizuno, H. & Ikeda, A. in Low-Temperature Thermal and Vibrational Properties of Disordered Solids (ed. Ramos, M.) Ch. 10 (World Scientific, 2022).

  50. Kriuchevskyi, I., Wittmer, J. P., Meyer, H. & Baschnagel, J. Shear modulus and shear-stress fluctuations in polymer glasses. Phys. Rev. Lett. 119, 147802 (2017).

    Article  ADS  Google Scholar 

  51. Lemaître, A. & Maloney, C. Sum rules for the quasi-static and visco-elastic response of disordered solids at zero temperature. J. Stat. Phys. 123, 415 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  52. Furukawa, A. & Tanaka, H. Direct evidence of heterogeneous mechanical relaxation in supercooled liquids. Phys. Rev. E 84, 061503 (2011).

    Article  ADS  Google Scholar 

  53. Rocklin, D. Z., Hsiao, L., Szakasits, M., Solomon, M. J. & Mao, X. Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity. Soft Matter 17, 6929–6934 (2021).

    Article  ADS  Google Scholar 

  54. Bonacci, F. et al. Contact and macroscopic ageing in colloidal suspensions. Nat. Mater. 19, 775–780 (2020).

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  57. Zhang, H., Zhang, Q., Liu, F. & Han, Y. Anisotropic-isotropic transition of cages at the glass transition. Phys. Rev. Lett. 132, 078201 (2024).

    Article  MathSciNet  Google Scholar 

  58. Cheng, Y. Q. & Ma, E. Configurational dependence of elastic modulus of metallic glass. Phys. Rev. B 80, 064104 (2009).

    Article  ADS  Google Scholar 

  59. Jabbari-Farouji, S., Tanaka, H., Wegdam, G. H. & Bonn, D. Multiple nonergodic disordered states in Laponite suspensions: a phase diagram. Phys. Rev. E 78, 061405 (2008).

    Article  ADS  Google Scholar 

  60. Goodrich, C. P., Liu, A. J. & Nagel, S. R. The principle of independent bond-level response: tuning by pruning to exploit disorder for global behavior. Phys. Rev. Lett. 114, 225501 (2015).

    Article  ADS  Google Scholar 

  61. Shen, X. et al. Achieving adjustable elasticity with non-affine to affine transition. Nat. Mater. 20, 1635–1642 (2021).

    Article  ADS  Google Scholar 

  62. Tateno, M. & Tanaka, H. Numerical prediction of colloidal phase separation by direct computation of Navier–Stokes equation. npj Comput. Mater. 5, 40 (2019).

    Article  ADS  Google Scholar 

  63. Wang, X., Ramírez-Hinestrosa, S., Dobnikar, J. & Frenkel, D. The Lennard–Jones potential: when (not) to use it. Phys. Chem. Chem. Phys. 22, 10624–10633 (2020).

    Article  Google Scholar 

  64. Schröder-Turk, G. E. et al. Disordered spherical bead packs are anisotropic. Europhys. Lett. 90, 34001 (2010).

    Article  ADS  Google Scholar 

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Acknowledgements

H.T. acknowledges the support by the Grant-in-Aid for Specially Promoted Research (JSPS KAKENHI Grant No. JP20H05619) from the Japan Society for the Promotion of Science (JSPS). M.T. acknowledges the support from JSPS KAKENHI (Grant No. JP20K14424). Y.W. acknowledges the support from Shanghai Jiao Tong University via the scholarship for outstanding PhD graduates. We thank the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo, for the use of the facilities.

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Authors and Affiliations

  1. Research Center for Advanced Science and Technology, The University of Tokyo, Meguro-ku, Japan

    Yinqiao Wang, Michio Tateno & Hajime Tanaka

  2. Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo, Meguro-ku, Japan

    Hajime Tanaka

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H.T. designed and supervised the project. Y.W. performed research. Y.W. and M.T. analysed data. All authors discussed the results and wrote the paper.

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Correspondence to Hajime Tanaka.

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Extended data

Extended Data Fig. 1 Snapshots of the gelation process.

Particles are colour-coded to differentiate those in the foreground from those in the background.

Extended Data Fig. 2 Self-intermediate scattering functions of glasses and gels.

a, Self-intermediate scattering function Fs(k, Δt, tw) for glasses at different ages (tw/τB = 9.6 × 101, 9.6 × 102, 9.6 × 103, 9.6 × 104, 9.6 × 105), depicted from left to right. Here, k is the peak wavenumber of the structural factor. b, Fs(k, Δt, tw) of all particles (dashed lines) and only isostatic particles (solid lines) for gels at different ages (tw/τB = 102, 103, 104, 105, 106), shown from left to right. The vertical dashed lines in a and b indicate the period of oscillatory deformation used in measuring the moduli of glasses and gels, respectively.

Extended Data Fig. 3 Ageing dynamics and observation-time-dependent elasticity in glasses with the Lennard-Jones potential (LJ glasses) and gels with the Wang-Frenkel potential (WF gels).

a, Illustration of the typical structure of an LJ glass. Particles are colour-coded based on their sizes. b, MSD \({\langle {\Delta} r^2 \rangle}\) versus observation time Δt for LJ glasses at different ageing time, tw. Here, the time unit is scaled by the Brownian time, τB. c, Observation-time-dependent shear modulus G and bulk modulus K of LJ glasses. Short bars indicate the affine moduli, GA and KA. d, Illustration of the typical structure of a WF gel. Particles are colour-coded based on their sizes. e, MSD of all particles \(\langle \Delta r^2 \rangle\) (dashed curves) and only isostatic particles \({\langle \Delta r^2 \rangle}_{\rm{iso}}\) (solid curves) versus Δt for WF gels at various tw. f, Observation-time-dependent shear modulus G and bulk modulus K of WF gels. Inset: the same data as the main panel with the vertical axis zoomed out to show the affine moduli GA and KA, as indicated by the short bars. The same plot as the Fig. 1 in the main text.

Extended Data Fig. 4 Amplitude and frequency sweep moduli in gels.

a, Shear stress σxy versus time t/Δt under oscillatory shear strain ϵxy (solid blue curve), where Δt is the period time. The black points represent individual σxy, and the red curve represents the fitting results using \({\sigma }_{xy}={\sigma }_{0}\sin (\omega t+\delta )\). b, Strain amplitude γ sweep of storage shear modulus \({G}^{{\prime} }\) and loss shear modulus G″. c, Frequency ω = 2π/(Δt/τB) sweep of \({G}^{{\prime} }\) and G″. d, Pressure p and volumetric strain ϵb versus t/Δt under oscillatory uniform compression ϵb (blue solid curve). The red curve represents the fitting results using \(p={p}_{0}\sin (\omega t+\delta )+{p}_{{{{\rm{c}}}}}\), where pc is the initial pressure of the system. e, Volume strain amplitude γb sweep of storage bulk modulus \({K}^{{\prime} }\) and loss bulk modulus K″. f, Frequency ω = 2π/(Δt/τB) sweep of \({K}^{{\prime} }\) and K″. The vertical dashed lines mark the amplitude and frequency used to measure the moduli in Fig. 2d–f. In this work, G and K refer specifically to the storage moduli \({G}^{{\prime} }\) and \({K}^{{\prime} }\).

Extended Data Fig. 5 Schematic representation of the observation-time (Δt) or frequency (ω)-dependent shear modulus.

The levels of affine (GA) and plateau shear moduli (Gp) are indicated on the left axis.

Extended Data Fig. 6 Age-dependent elasticity in LJ glasses and WF gels.

The age-dependent thermal elasticity G (a,d), K (b,e), modulus ratio G/K and Poisson ratio ν (c,f) (red circles) and corresponding inherent elasticity at zero temperature (blue squares) in LJ glasses (a–c) and WF gels (d–f). The observation time Δt used to measure these moduli are marked by the vertical dashed lines in Extended Data Fig. 3. The same plot as the Fig. 2 in the main text.

Extended Data Fig. 7 Scaled moduli versus mean-squared displacement (MSD) in glasses and gels.

a, Shear modulus G scaled by the affine modulus GA (infinite-frequency modulus) versus the inverse of MSD \({\langle \Delta {r}^{2}\rangle }^{-1}\) in glasses. b, Shear modulus G scaled by GA versus the inverse of isostatic MSD \({\langle \Delta {r}^{2}\rangle }_{{{{\rm{iso}}}}}^{-1}\) in gels. c, Scaled shear modulus G/GIS versus MSD \({\langle \Delta {r}^{2}\rangle }_{{{{\rm{rel}}}}}^{-1}\) in glasses. d, Scaled shear modulus G/GIS and bulk modulus K/KIS versus MSD of isostatic particles \({\langle \Delta {r}^{2}\rangle }_{{{{\rm{iso}}}},{{{\rm{rel}}}}}^{-1}\) in gels. e, Scaled shear modulus G/GIS and bulk modulus K/KIS versus original MSD of all particles \({\langle \Delta {r}^{2}\rangle }^{-1}\) in gels.

Extended Data Fig. 8 Role of inherent elasticity and MSD on thermal elasticity in the LJ glasses and WF gels.

a, Inverse MSD \(\langle \Delta r^2\rangle^{-1}\) of LJ glasses at different observation times Δt plotted against scaled waiting time tw/τB. b, Ratios between thermal elasticity and inherent elasticity M/MIS of LJ glasses versus tw/τB for different Δt. c, Scaled shear modulus G/GIS of LJ glasses versus \(\langle \Delta r^2\rangle^{-1}\) for different Δt. d, Inverse MSD of isostatic particles \((Z\geq6)\) \({\langle \Delta r^2\rangle}^{-1}_{\rm{iso}}\) of WF gels versus tw/τB for different Δt. e,f, G/GIS and K/KIS of WF gels versus tw/τB (e) and \({\langle \Delta r^2\rangle}^{-1}_{\rm{iso}}\) (f) for different Δt. The same plot as the Fig. 3 in the main text.

Extended Data Fig. 9 Age-dependent structure of glasses in inherent states.

a, Orientational order parameter Ω and cage anisotropy parameter η. b, Pressure p. Note that the scales of all vertical axes are the same as those shown for the corresponding structural parameters in Fig. 4 in the main text.

Extended Data Fig. 10 Age-dependent potential energy and structure in the LJ glasses and WF gels.

a, Age-dependent potential energy per particle (red open circles), E, and per contact (blue open squares), 2E/Z, in LJ glasses. b, Age-dependent orientational order parameter and Ω anisotropy parameter η of Voronoi cells in LJ glasses, where Ω = 0 indicates perfect order and η = 1 indicates isotropic cells. c, Age-dependent pressure p in LJ glasses. d, The same as in a, for WF gels. e, Age-dependent contact number Z in WF gels. f, Age-dependent loop number Nloop in WF gels. The same plot as the Fig. 4 in the main text.

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Wang, Y., Tateno, M. & Tanaka, H. Distinct elastic properties and their origins in glasses and gels. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02456-6

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