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.

  • Letter
  • Published:

A thermodynamic connection to the fragility of glass-forming liquids

Nature volume 410, pages 663–667 (2001)Cite this article

Abstract

Although liquids normally crystallize on cooling, there are members of all liquid types (including molecular, ionic and metallic) that supercool and then solidify at their glass transition temperature, Tg. This continuous solidification process exhibits great diversity within each class of liquid—both in the steepness of the viscosity–temperature profile, and in the rate at which the excess entropy of the liquid over the crystalline phase changes as Tg is approached. However, the source of the diversity is unknown. The viscosity and associated relaxation time behaviour have been classified between ‘strong’ and ‘fragile’ extremes, using Tg as a scaling parameter1, but attempts to correlate such kinetic properties with the thermodynamic behaviour have been controversial2,3. Here we show that the kinetic fragility can be correlated with a scaled quantity representing excess entropy, using data over the entire fragility range and embracing liquids of all classes. The excess entropy used in our correlation contains both configurational and vibration-related contributions. In order to reconcile our correlation with existing theory and simulations, we propose that variations in the fragility of liquids originate in differences between their vibrational heat capacities, harmonic and anharmonic, which we interpret in terms of an energy landscape. The differences evidently relate to behaviour of low-energy modes near and below the boson peak.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 2: Plots of scaled excess entropy versus Tg-scaled inverse temperature.
Figure 1: Tg-scaled Arrhenius plot for liquids of every class for which thermodynamic data are also available.
Figure 3: Correlation of the thermodynamic and kinetic F1/2 fragilities from Figs 1 and 2.
Figure 4: Graphical explanation of how high liquid fragility originates in the change of energy landscape ‘basin shape’ (hence of the vibrational density of states) during thermal excitation to high potential energies.

Similar content being viewed by others

References

  1. Angell, C. A. Relaxation in liquids, polymers and plastic crystals - strong/fragile patterns and problems. J. Non-Cryst. Solids 131-133, 13–31 (1991).

    Article  ADS  CAS  Google Scholar 

  2. Ito, K., Moynihan, C. T. & Angell, C. A. Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water. Nature 398, 492–495 (1999).

    Article  ADS  CAS  Google Scholar 

  3. Ngai, K. L. & Yamamuro, O. Thermodynamic fragility and kinetic fragility in supercooled liquids: a missing link. J. Chem. Phys. 111, 10403–10406 (1999).

    Article  ADS  CAS  Google Scholar 

  4. Sastry, S., Debenedetti, P. G. & Stillinger, F. H. Signatures of distinct dynamical regimes in the energy landscape of a glassforming liquid. Nature 393, 554–557 (1998).

    Article  ADS  CAS  Google Scholar 

  5. Speedy, R. J. Relations between a liquid and its glasses. J. Phys. Chem. B 103, 4060–4065 (1999).

    Article  CAS  Google Scholar 

  6. Roland, C. M., Santangelo, P. G. & Ngai, K. L. The application of the energy landscape model to polymers. J. Chem. Phys. 111, 5593–5598 (1999).

    Article  ADS  CAS  Google Scholar 

  7. Speedy, R. J. The hard sphere glass transition. Mol. Phys. 95, 169–178 (1998).

    Article  ADS  CAS  Google Scholar 

  8. Sciortino, F., Kob, W. & Tartaglia, P. Inherent structure entropy of supercooled liquids. Phys. Rev. Lett. 83, 3214–3217 (1999).

    Article  ADS  CAS  Google Scholar 

  9. Buechner, S. & Heuer, A. The potential energy landscape of a model glassformer: thermodynamics, anharmonicities, and finite size effects. Phys. Rev. E 60, 6507–6518 (1999).

    Article  ADS  Google Scholar 

  10. Coluzzi, B., Verrocchio, P., Mezard, M. & Parisi, G. Lennard-Jones binary mixture: a thermodynamical approach to glass transition. J. Chem. Phys. 112, 2933–2944 (2000).

    Article  ADS  CAS  Google Scholar 

  11. Scala, A., Starr, F., La Nave, E., Sciortino, F. & Stanley, H. E. Configurational entropy and diffusion of supercooled water. Nature 406, 166–169 (2000).

    Article  ADS  CAS  Google Scholar 

  12. Sastry, S. Liquid limits: the glass transition and liquid-gas spinodal boundaries of metastable liquids. Phys. Rev. Lett. 85, 590–593 (2000).

    Article  ADS  CAS  Google Scholar 

  13. Sastry, S. The relationship between fragility, configurational entropy and the potential energy landscape of glassforming liquids. Nature 409, 164–167 (2001).

    Article  ADS  CAS  Google Scholar 

  14. Richet, P. Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471–483 (1984).

    Article  ADS  CAS  Google Scholar 

  15. Richet, P. & Bottinga, Y. Glass transitions and thermodynamic properties of amorphous SiO2, NaAlSinO2n+2 and KAlSi3O8. Geochim. Cosmochim. Acta 48, 453–470 (1984).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  17. Angell, C. A. Entropy and fragility in supercooled liquids. J. Res. NIST 102, 171–185 (1997).

    Article  CAS  Google Scholar 

  18. Richert, R. & Angell, C. A. Dynamics of glassforming liquids. IV: On the link between molecular dynamics and configurational entropy. J. Chem. Phys. 108, 9016–9026 (1998).

    Article  ADS  CAS  Google Scholar 

  19. Goldstein, M. Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 51, 3728–3729 (1969).

    Article  ADS  CAS  Google Scholar 

  20. Stillinger, F. H. & Weber, T. A. Packing structures and transitions in liquids and solids. Science 225, 983–989 (1984).

    Article  ADS  CAS  Google Scholar 

  21. Goldstein, M. Viscous liquids and the glass transition: sources of the excess heat capacity. J. Chem. Phys. 64, 4767–4773 (1976).

    Article  ADS  CAS  Google Scholar 

  22. Johari, G. P. Contributions to the entropy of a glass and liquid, and the dielectric relaxation time. J. Chem. Phys. 112, 7518–7523 (2000).

    Article  ADS  CAS  Google Scholar 

  23. Greet, R. J. & Turnbull, D. Test of Adam-Gibbs liquid viscosity model with o-terphenyl specific-heat data. J. Chem. Phys. 47, 2185–2190 (1967).

    Article  ADS  CAS  Google Scholar 

  24. Magill, J. H. Physical properties of aromatic hydrocarbons. III. A test of the Adam-Gibbs relaxation model for glass formers based on the heat-capacity data of 1,3,5-tri-α-naphthylbenzene. J. Chem. Phys. 47, 2802–2807 (1967).

    Article  ADS  CAS  Google Scholar 

  25. Takahara, S., Yamamuro, O. & Suga, H. Heat capacities and glass transitions of 1-propanol and 3-methyl pentane: new evidence for the entropy theory. J. Non-Cryst. Solids 171, 259–270 (1994).

    Article  ADS  CAS  Google Scholar 

  26. Takahara, S., Yamamuro, O. & Matsuo, T. Calorimetric study of 3-bromopentane—correlation between structural relaxation time and configurational entropy. J. Phys. Chem. 99, 9580–9592 (1995).

    Article  Google Scholar 

  27. Angell, C. A. Liquid landscapes. Nature 393, 521–522 (1998).

    Article  ADS  CAS  Google Scholar 

  28. Starr, F. W. et al. Thermodynamic and structural aspects of the potential energy surface of simulated water. Phys. Rev. E. (in the press); also preprint arXiv:cond-mat/0007487 on http://xxx.lanl.gov/ (2000).

  29. Phillips, W. A., Buchenau, U., Nücker, N., Dianou, A. J. & Petry, W. Dynamics of glassy and liquid selenium. Phys. Rev. Lett. 63, 2381–2384 (1989).

    Article  ADS  CAS  Google Scholar 

  30. Wischnewski, A., Buchenau, U., Dianoux, A. J., Kamitakahara, W. A. & Zarestky, J. L. Neutron scattering analysis of low-frequency modes in silica. Phil. Mag. B 77, 579–589 (1998).

    Article  ADS  CAS  Google Scholar 

  31. Kob, W., Sciortino, F. & Tartaglia, P. Aging as dynamics in configuration space. Europhys. Lett. 49, 590–596 (2000).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank S. Sastry, R. Speedy and F. Sciortino for comments and criticisms. This work was supported by the NSF, Division of Materials Research, Solid State Chemistry program.

Author information

Authors and Affiliations

  1. Department of Chemistry and Biochemistry, Arizona State University, Tempe, 85287-1604, Arizona, USA

    L.-M. Martinez & C. A. Angell

Authors
  1. L.-M. Martinez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. A. Angell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. A. Angell.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martinez, LM., Angell, C. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663–667 (2001). https://doi.org/10.1038/35070517

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35070517

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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