Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water

Abstract

If crystallization can be avoided when a liquid is cooled, it will typically form a glass. Near the glass transition temperature the viscosity increases continuously but rapidly with cooling. As the glass forms, the molecular relaxation time increases with an Arrhenius-like (simple activated) form in some liquids, but shows highly non-Arrhenius behaviour in others. The former are said to be ‘strong’ liquids, and the latter ‘fragile’1,2. Here we show that the fragility of a liquid can be determined from purely thermodynamic data (as opposed to measurements of kinetics) near and below the melting point. We find that for most liquids the fragilities estimated this way are consistent with those obtained by previous methods and by a new method (ref. 3 and K.I., C.A.A. and C.T.M., unpublished data) at temperatures near the glass transition. But water is an exception. The thermodynamic method indicates that near its melting point it is the most fragile of all liquids studied, whereas the kinetic approach indicates that near the glass transition it is the least fragile. We propose that this discrepancy can be explained by a fragile-to-strong transition in supercooled water near 228 K, corresponding to a change in the liquid's structure at this point.

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Figure 1: Use of the Kauzmann plot to define thermodynamic fragility for glass-forming liquids.
Figure 2: Correlation between fragility metrics ΔTg/ Tg and F1/2.

References

  1. 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).

    ADS  Article  Google Scholar 

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

    Moynihan, C. T. Correlation between the width of the glass transition and the temperature dependence of the viscosity in high Tgglasses. J. Am. Ceram. Soc. 76, 1081–1087 (1993).

    CAS  Article  Google Scholar 

  4. 4

    Kauzmann, W. The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43, 219–256 (1948).

    CAS  Article  Google Scholar 

  5. 5

    Angell, C. A. & Tucker, J. C. Heat capacities and fusion entropies of the tetrahydrates of calcium nitrate, cadmium nitrate, and magnesium acetate. Concordance of calorimetric and relaxational ‘ideal’ glass transition temperatures. J. Phys. Chem. 78, 278– 281 (1974).

    CAS  Article  Google Scholar 

  6. 6

    Xu, Y. & Heppler, L. Calorimetric investigations of crystalline, molten, and supercooled Ca(NO3)2·4H2O and of concentrated Ca(NO3)2(aq). J. Chem. Thermodyn. 25, 91–97 ( 1993).

    CAS  Article  Google Scholar 

  7. 7

    Angell, C. A. et al. Liquid fragility and the glass transition in water and aqueous solutions. Int. J. Food Sci. 22, 115– 142 (1994).

    Google Scholar 

  8. 8

    Takahara, S., Yamamuro, O. & Matsuo, T. Calorimetric study of 3-bromopentane: correlation between structural relaxation time and configurational entropy. J. Phys. Chem. 99, 9589–9592 ( 1995).

    CAS  Article  Google Scholar 

  9. 9

    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).

    ADS  CAS  Article  Google Scholar 

  10. 10

    Chang, S. S. & Bestul, A. b. Heat capacities of selenium crystal (trigonal), glass, and liquid from 5 to 360 K. J. Chem. Thermodyn. 6, 325–344 ( 1974).

    CAS  Article  Google Scholar 

  11. 11

    Gibbs, J. H. in Modern Aspects of the Vitreous State(ed. McKenzie, J. D.) Ch. 7 (Butterworths, London, (1960).

    Google Scholar 

  12. 12

    Goldstein, M. Viscous liquids and the glass transition. IV. Thermodynamic equations and the transition. J. Phys. Chem. 77, 667– 673 (1973).

    CAS  Article  Google Scholar 

  13. 13

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

    ADS  CAS  Article  Google Scholar 

  14. 14

    Angell, C. A., Shuppert, J. & Tucker, J. C. Anomalous properties of supercooled water: heat capacity, expansivity, and PMR chemical shift from 0 to −38 °C. J. Phys. Chem. 77, 3092–3099 (1973).

    CAS  Article  Google Scholar 

  15. 15

    Donth, E. The size of cooperative rearranging region at the glass transition. J. Non-Cryst. Solids 53, 325–330 (1982).

    ADS  CAS  Article  Google Scholar 

  16. 16

    Hodge, I. M. Comment on the fragility of liquids—a brief critique. J. Non-Cryst. Solids 202, 164–172 (1997).

    ADS  Article  Google Scholar 

  17. 17

    Angell, C. A. Simple glassformers: their definition, fragilities and landscape excitation profiles. J. Phys., Cond. Matter 11, 75– 94 (1999).

    Article  Google Scholar 

  18. 18

    Angell, C. A. & Sare, E. J. Glass-forming composition regions and glass transition temperatures for aqueous electrolyte solutions. J. Chem. Phys. 52, 1058–1068 (1970).

    ADS  CAS  Article  Google Scholar 

  19. 19

    Angell, C. A. & Tucker, J. C. Heat capacity changes in glass-forming aqueous solutions, and the glass transition in vitreous water. J. Phys. Chem. 84, 268–272 (1980).

    CAS  Article  Google Scholar 

  20. 20

    Johari, G., Hallbrucker, A. & Mayer, E. The glass-liquid transition of hyperquenched water. Nature 330, 552–553 (1987).

    ADS  CAS  Article  Google Scholar 

  21. 21

    Hallbrucker, A., Mayer, E. & Johari, G. P. Glass-liquid transition and the enthalpy of devitrification of annealed vapor-deposited amorphous water. A comparison with hyperquenched glassy water. J. Phys. Chem. 93, 4986– 4990 (1989).

    CAS  Article  Google Scholar 

  22. 22

    Angell, C. A., Clarke, J. H. R. & Woodcock, L. V. Interaction potentials and glass formation: A survey of computer experiments. Adv. Chem. Phys. 48, 397–453 (1981).

    CAS  Google Scholar 

  23. 23

    Hofer, K., Mayer, E. & Johari, G. P. Glass-liquid transition of water and ethylene glycol solution in poly(2-hydroxyethyl methacrylate) hydrogel. J. Phys. Chem. 94, 2689–2696 ( 1990).

    CAS  Article  Google Scholar 

  24. 24

    Speedy, R. J. & Angell, C. A. Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at 45 °C. J. Chem. Phys. 65, 851– 858 (1976).

    ADS  CAS  Article  Google Scholar 

  25. 25

    Sastry, S., Debenedetti, P. G., Sciortino, F. & Stanley, H. E. Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E 53, 6144– 6154 (1996).

    ADS  CAS  Article  Google Scholar 

  26. 26

    Thompson, M. O., Galvin, G. J. & Mayer, J. W. Melting temperatures and explosive crystallization of amorphous silicon during pulsed laser irradiation. Phys. Rev. Lett. 52, 2360–2363 ( 1984).

    ADS  CAS  Article  Google Scholar 

  27. 27

    Angell, C. A. & Borick, S. Comment on “Structure of Supercooled Liquid Silicon” by Ansell et al. J. Phys., Cond. Matter (in the press).

  28. 28

    Brückner, R. Metastable equilibrium density of hydroxyl-free synthetic vitreous silica. J. Non-Cryst. Solids 5, 281– 285 (1971).

    ADS  Article  Google Scholar 

  29. 29

    Rebelo, L. P. N., Debenedetti, P. G. & Sastry, S. Singularity-free interpretation of the thermodynamics of supercooled water. II. Thermal and volumetric behavior. J. Chem. Phys. 109, 626–633 ( 1998).

    ADS  CAS  Article  Google Scholar 

  30. 30

    Starr, F., Angell, C. A., Speedy, R. J. & Stanley, H. E. Entropy and dynamic properties of water at 1 atm in the “experimentally-inaccessible” region between 150K and 236K Phys. Rev. Lett. (submitted).

  31. 31

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

    ADS  CAS  Article  Google Scholar 

  32. 32

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

    CAS  Article  Google Scholar 

  33. 33

    Angell, C. A., Finch, E. D., Woolf, L. A. & Bach, P. Spin-echo diffusion coefficients of water to 2380 bar and −20 °C. J. Chem. Phys. 65, 3063– 3066 (1976).

    ADS  CAS  Article  Google Scholar 

  34. 34

    Allegra, J. C., Stein, A. & Allen, G. F. Tracer diffusion and shear viscosity for the system isobutyric acid-water near the critical mixing point. J. Chem. Phys. 55, 1716–1720 ( 1971).

    ADS  CAS  Article  Google Scholar 

  35. 35

    Smith, R. S., Huang, C. & Kay, B. D. Evidence for molecular translational diffusion, during the crystallization of amorphous solid water. J. Phys. Chem. B 101, 6123–6126 ( 1997).

    CAS  Article  Google Scholar 

  36. 36

    Smith, R. S. & Kay, B. D. Evidence for the existence of supercooled liquid water at 150 K. Nature 398(in the press)

  37. 37

    Roberts, C. J., Karayiannekis, C. & Debenedetti, P. G. Liquid-liquid immiscibility in single-component network-forming fluids: Model calculations and implications for polyamorphism in water. Ind. Eng. Chem. Res. 37, 3012–3022 (1998).

    CAS  Article  Google Scholar 

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Acknowledgements

This work was supported by the NSF DMR Solid State Chemistry program.

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Correspondence to C. Austen Angell.

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Ito, K., Moynihan, C. & Angell, C. Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water. Nature 398, 492–495 (1999). https://doi.org/10.1038/19042

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