Hierarchical aging pathways and signatures of thermodynamic transition in molecular glasses

  • Shiyu Liu (刘诗宇)
  • Yao Yu (于尧)Email author
  • Lin Liu (柳林)
  • Yue Wu (吴跃)Email author


When a liquid is supercooled, its structural equilibration time τeq increases sharply approaching the glass transition temperature Tg, below which it is kinetically arrested in the out of equilibrium glassy state. Upon annealing below Tg, such glassy state relaxes toward the equilibrium state. There is growing evidence that such relaxation process is quite complex, influenced by the complexity of the potential energy landscape. Here we report the observation of a hierarchical aging pathway in the process of the glass-to-supercooled liquid transition in various molecular glass forming systems. Differential scanning calorimetry reveals that the glassy state upon annealing below Tg firstly enters a transient metastable supercooled liquid state with slightly higher enthalpies than that of the equilibrium supercooled liquid state when extrapolated to below Tg. This observation is also confirmed by structural measurements via Raman scattering. The dynamics of the transient metastable-to-stable supercooled liquid transition exhibits characteristics of thermodynamic transition at spinodal temperature Tsp slightly above Tg, leading to anomalous behaviors such as the appearance of a transition-like behavior in the plot of fragility measurements. These observations imply that the free energy landscape of the supercooled liquid develops complexity with qualitative changes approaching Tg and could have strong influence on the process of the glass transition.


glass transition hierarchical aging pathways thermodynamic transition metastability 



当液体被过冷, 液体的结构平衡时间τeq在接近玻璃化转变温度Tg附近时迅速增加, 使得液体在温度降到Tg以下时从动力学角度看束缚在非平衡的玻璃态中. 当在Tg以下退火时, 这个玻璃态逐渐弛豫到平衡态. 越来越多的证据表明这个弛豫的过程非常复杂, 而且受到势能景图的影响. 本文通过研究不同的小分子玻璃形成系统发现从玻璃转变到过冷液体的过程中出现了一个分层的老化路径. 通过差示扫描量热仪实验发现在Tg以下退火时, 玻璃态先进入到一个暂时的亚稳态过冷液体. 在Tg以下, 这个液体的焓值稍微比平衡态过冷液体高. 通过拉曼散射测量结构的实验同样证实了这个发现. 这个暂时的亚稳态到稳态过冷液体的转变动力学在温度Tsp处表现出了热力学转变的特征, 并且导致了一系列反常现象比如在脆性指数图上出现的类相变行为. 这些发现暗示了过冷液体的自由能景图在接近Tg的时候变得复杂而且具有质的变化, 同时对玻璃化转变过程有很明显的影响.



This work was partially supported by the National Basic Research Program of China (2015CB856801). We are grateful to the Analytical and Testing Center, Huazhong University of Science and Technology for technical assistance.

Supplementary material

40843_2018_9382_MOESM1_ESM.pdf (1004 kb)
Hierarchical aging pathways and signatures of thermodynamic transition in molecular glasses


  1. 1.
    Ediger MD, Angell CA, Nagel SR. Supercooled liquids and glasses. J Phys Chem, 1996, 100: 13200–13212CrossRefGoogle Scholar
  2. 2.
    Angell CA. Formation of glasses from liquids and biopolymers. Science, 1995, 267: 1924–1935CrossRefGoogle Scholar
  3. 3.
    Berthier L, Biroli G. Theoretical perspective on the glass transition and amorphous materials. Rev Mod Phys, 2011, 83: 587–645CrossRefGoogle Scholar
  4. 4.
    Dyre JC. Colloquium: The glass transition and elastic models of glass-forming liquids. Rev Mod Phys, 2006, 78: 953–972CrossRefGoogle Scholar
  5. 5.
    Chandler D, Garrahan JP. Dynamics on the way to forming glass: bubbles in space-time. Annu Rev Phys Chem, 2010, 61: 191–217CrossRefGoogle Scholar
  6. 6.
    Cavagna A. Supercooled liquids for pedestrians. Phys Rep, 2009, 476: 51–124CrossRefGoogle Scholar
  7. 7.
    Swallen SF, Kearns KL, Mapes MK, et al. Organic glasses with exceptional thermodynamic and kinetic stability. Science, 2007, 315: 353–356CrossRefGoogle Scholar
  8. 8.
    Lubchenko V, Wolynes PG. Theory of structural glasses and supercooled liquids. Annu Rev Phys Chem, 2007, 58: 235–266CrossRefGoogle Scholar
  9. 9.
    Hecksher T, Nielsen AI, Olsen NB, et al. Little evidence for dynamic divergences in ultraviscous molecular liquids. Nat Phys, 2008, 4: 737–741CrossRefGoogle Scholar
  10. 10.
    Zhao J, Simon SL, McKenna GB. Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems. Nat Commun, 2013, 4: 1783CrossRefGoogle Scholar
  11. 11.
    Mauro JC, Yue Y, Ellison AJ, et al. Viscosity of glass-forming liquids. Proc Natl Acad Sci USA, 2009, 106: 19780–19784CrossRefGoogle Scholar
  12. 12.
    Moynihan CT. Structural relaxation and the glass transition. Rev Mineral Geochem, 1995, 32: 1–19Google Scholar
  13. 13.
    Moynihan CT, Easteal AJ, Wilder J, et al. Dependence of the glass transition temperature on heating and cooling rate. J Phys Chem, 1974, 78: 2673–2677CrossRefGoogle Scholar
  14. 14.
    Moynihan CT. Correlation between the width of the glass transition region and the temperature dependence of the viscosity of high-Tg glasses. J Am Ceramic Soc, 1993, 76: 1081–1087CrossRefGoogle Scholar
  15. 15.
    Böhmer R, Ngai KL, Angell CA, et al. Nonexponential relaxations in strong and fragile glass formers. J Chem Phys, 1993, 99: 4201–4209CrossRefGoogle Scholar
  16. 16.
    Wimberger-Friedl R, de Bruin JG. The very long-term volume recovery of polycarbonate: is self-retardation finite? Macromolecules, 1996, 29: 4992–4997CrossRefGoogle Scholar
  17. 17.
    Luo P, Wen P, Bai HY, et al. Relaxation decoupling in metallic glasses at low temperatures. Phys Rev Lett, 2017, 118: 225901CrossRefGoogle Scholar
  18. 18.
    Gallino I, Cangialosi D, Evenson Z, et al. Hierarchical aging pathways and reversible fragile-to-strong transition upon annealing of a metallic glass former. Acta Mater, 2018, 144: 400–410CrossRefGoogle Scholar
  19. 19.
    Goldstein M. Viscous liquids and the glass transition: a potential energy barrier picture. J Chem Phys, 1969, 51: 3728–3739CrossRefGoogle Scholar
  20. 20.
    Charbonneau P, Kurchan J, Parisi G, et al. Fractal free energy landscapes in structural glasses. Nat Commun, 2014, 5: 3725CrossRefGoogle Scholar
  21. 21.
    Kubaschewski O, Alcock CB, Spencer P. Materials Thermochemistry. Oxford: Pergamon Press, 1993Google Scholar
  22. 22.
    Tool AQ. Relation between inelastic deformability and thermal expansion of glass in its annealing range. J Am Ceramic Soc, 1946, 29: 240–253CrossRefGoogle Scholar
  23. 23.
    Narayanaswamy OS. A model of structural relaxation in glass. J Am Ceramic Soc, 1971, 54: 491–498CrossRefGoogle Scholar
  24. 24.
    Debolt MA, Easteal AJ, Macedo PB, et al. Analysis of structural relaxation in glass using rate heating data. J Am Ceramic Soc, 1976, 59: 16–21CrossRefGoogle Scholar
  25. 25.
    Crowley KJ, Zografi G. The use of thermal methods for predicting glass-former fragility. ThermoChim Acta, 2001, 380: 79–93CrossRefGoogle Scholar
  26. 26.
    Chen Z, Zhao L, Tu W, et al. Dependence of calorimetric glass transition profiles on relaxation dynamics in non-polymeric glass formers. J Non-Crystalline Solids, 2016, 433: 20–27CrossRefGoogle Scholar
  27. 27.
    Freer AA, Bunyan JM, Shankland N, et al. Structure of (S)- (+)-ibuprofen. Acta Crystlogr C Cryst Struct Commun, 1993, 49: 1378–1380CrossRefGoogle Scholar
  28. 28.
    Bras AR, Noronha JP, Antunes AMM, et al. Molecular motions in amorphous ibuprofen as studied by broadband dielectric spectroscopy. J Phys Chem B, 2008, 112: 11087–11099CrossRefGoogle Scholar
  29. 29.
    Badrinarayanan P, Zheng W, Li Q, et al. The glass transition temperature versus the fictive temperature. J Non-Crystalline Solids, 2007, 353: 2603–2612CrossRefGoogle Scholar
  30. 30.
    Hodge IM, Berens AR. Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 2. Mathematical modeling. Macromolecules, 1982, 15: 762–770CrossRefGoogle Scholar
  31. 31.
    Wolynes PG. Spatiotemporal structures in aging and rejuvenating glasses. Proc Natl Acad Sci USA, 2009, 106: 1353–1358CrossRefGoogle Scholar
  32. 32.
    Debenedetti PG, Stillinger FH. Supercooled liquids and the glass transition. Nature, 2001, 410: 259–267CrossRefGoogle Scholar
  33. 33.
    Palmer RG. Broken ergodicity. Adv Phys, 1982, 31: 669–735CrossRefGoogle Scholar
  34. 34.
    Binder K. Nucleation barriers, spinodals, and the Ginzburg criterion. Phys Rev A, 1984, 29: 341–349CrossRefGoogle Scholar
  35. 35.
    Vueba ML, Pina ME, Batista de Carvalho LAE. Conformational stability of ibuprofen: Assessed by DFT calculations and optical vibrational spectroscopy. J Pharmaceutical Sci, 2008, 97: 845–859CrossRefGoogle Scholar
  36. 36.
    Rossi B, Verrocchio P, Viliani G, et al. Vibrational properties of ibuprofen-cyclodextrin inclusion complexes investigated by Raman scattering and numerical simulation. J Raman Spectrosc, 2009, 40: 453–458CrossRefGoogle Scholar
  37. 37.
    Crupi V, Majolino D, Venuti V, et al. Temperature effect on the vibrational dynamics of cyclodextrin inclusion complexes: investigation by FTIR-ATR spectroscopy and numerical simulation. J Phys Chem A, 2010, 114: 6811–6817CrossRefGoogle Scholar
  38. 38.
    Nelson DR. Defects and Geometry in Condensed Matter Physics. Cambridge: Cambridge University Press, 2002Google Scholar
  39. 39.
    Kivelson D, Kivelson SA, Zhao X, et al. A thermodynamic theory of supercooled liquids. Phys A-Stat Mech Appl, 1995, 219: 27–38CrossRefGoogle Scholar
  40. 40.
    Kivelson D, Tarjus G. Apparent polyamorphism and frustration. J Non-Crystalline Solids, 2002, 307-310: 630–636CrossRefGoogle Scholar
  41. 41.
    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, 2012, 35: 113CrossRefGoogle Scholar
  42. 42.
    Nishio M. CH/τ hydrogen bonds in crystals. CrystEngComm, 2004, 6: 130–158CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Materials Science and Engineering and State Key Lab for Materials Processing and Die and Mold TechnologyHuazhong University of Science and TechnologyWuhanChina
  2. 2.Wuhan National High Magnetic Field CenterHuazhong University of Science and TechnologyWuhanChina
  3. 3.Department of Physics and AstronomyUniversity of North Carolina at Chapel HillChapel HillUSA

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