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Glass transition: A unified treatment

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Abstract

A unified kinetic and thermodynamic description of the glass transition in undercooled liquids at normal pressure is established. The following results are obtained for the first time: (1) The glass transition temperature Tg is determined to be in the range of Ts < Tg < Tn. Both Ts and Tn are material-dependent and each of them is characterized by a different Ω(T) = TΔslc(T)/Δslc(T) with Δhlc as the excess enthalpy and Δslc the excess entropy. (2) Being above Kauzmann’s isentropic temperature, the lowest limit Ts is determined by Ω(Ts) = 1 −2/(3γ) with γ being the ratio between the total energy and the free energy of the liquid-crystal interface. (3) Although a glass preserves the entropy and enthalpy values of the liquid at Tg, the ratio Ω(Tg) is found to be bound by a Tg-independent material constant 1 −2/(3γ). (4) Tg increases linearly with the logarithm of the cooling rate and such a linear relationship is found to be not always valid. (5) The observed cooling-rate dependent glass transition at Tg is the kinetically modified reflection of an underlying cooling-rate independent transition at Ts, and the underlying transition at Ts is kinetically equivalent to the sudden and strong divergence of the structure relaxation time of the liquid. (6) It is shown that if the cooling rate exceeds a minimum value determined here as a function of temperature, the atoms of an undercooled liquid will not have sufficient time to rearrange themselves into the corresponding crystalline configuration; consequently, crystalline nucleation can be prevented. The results are supported by the available experimental evidence. A systematic test of the results on different systems is possible since the results are in terms of experimentally accessible quantities.

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References

  1. S. R. Elliott, Physics of Amorphous Materials (Longman Scientific & Technical and John Wiley & Sons Inc., New York, 1992), Chap. 2.

    Google Scholar 

  2. R. Zallen, The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983).

    Book  Google Scholar 

  3. Dynamic Aspects of Structural Change in Liquids and Glasses, edited by C. A. Angell and M. Goldstein (New York Academy of Science, New York, 1986).

  4. W. Kauzmann, Chem. Rev. 43, 219 (1948).

    Article  CAS  Google Scholar 

  5. e.g., T.R. Kirkpatrick and P.G. Wolynes, Phys. Rev. A35, 3072 (1987); J. P. Sethna, Europhys. Lett. 6, 529 (1988); D.L. Stein and R.G. Palmer, Phys. Rev. B 38, 12035 (1988); T.A. Vilgid, Polym. Commun. 29, 327 (1988); J. P. Sethna, J. D. Shore, and M. Hung, Phys. Rev. B 44, 4943 (1991).

  6. For a brief survey of the microscopic models, see Ref. 1.

  7. J.H. Gibbs and E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958); G. Adam and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965); K.L. Ngai, R.W. Rendell, and D.J. Plazek, J. Chem. Phys. 94, 3018 (1991).

  8. M.H. Cohen and G.S. Grest, J. Non-Cryst. Solids 61/62, 749 (1984); M. H. Cohen and D. Turnbull, J. Chem. Phys. 34, 120 (1961); 52, 3038 (1970); F. Spaepen, in Physics of Defects, edited by R. Balian, M. Kleman, and J-P. Poirier (North-Holland, Amsterdam, 1981), p. 133.

  9. E. Leutheusser, Phys. Rev. A 29, 2765 (1984); W. Gotze and L. Sjogren, Rep. Prog. Phys. 55, 241 (1992); and references therein.

  10. e.g., D. Elderfield and D. Sherrington, J. Phys. C16, L497 L1169 (1983).

  11. e.g., T. V. Ramakrishnan and M. Yussouff, Phys. Rev. B 19, 2775 (1979); D. W. Oxtoby, in Liquids, Freezing and Glass Transition, edited by J. P. Hansen, D. Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, 1991); see also a review by A. D. J. Haymet, Ann. Rep. Phys. Chem. 38, 89 (1987).

  12. e.g., R. Zwanzig, Kinam 3, (1981); J. Joackle, Rep. Prog. Phys. 49, 171 (1986); F.H. Stillinger and L.J. Root, J. Chem. Phys. 89, 5081 (1988); D. Deng, A. S. Argon, and S. L. Yip, Philos. Trans. Roy. Soc. A329, 595 (1989); A. Vandenbeukel and J. Sietsma, Scripta Metall. et Mater. 38, 383 (1990); G.W. Scherer, J. Non-Cryst. Solids 123, 75 (1990); U. Mohanty, Physica A177, 345 (1991); J. Lewis, Phys. Rev. B 44, 4245 (1991); J. T. Bendler and M. F. Shlesinger, J. Phys. Chem. 96, 3970 (1992); S. F. Edwards, Int. J. Mod. Phys. B6, 1587 (1992); C. M. Roland and K. L. Ngal, Macromolec. 25, 5765 (1992); W. Kob and H. C. Andersen, Phys. Rev. E47, 3281 (1993); L.J. Lewis and G. Wahnstrom, Solid State Commun. 86, 295 (1993); G.P. Johari, J. Chem. Phys. 98, 7324 (1993); A. Hunt, J. Non-Cryst. Solids 160, 183 (1993); S. Dattagupta and L.A. Turski, Phys. Rev. E47, 1222 (1993); T.A. Vilgis, Phys. Rev. bf B47, 2882 (1993); R. Bohmer, K.L. Ngai, C.A. Angell, and D.J. Plazek, J. Chem. Phys. 48, 4201 (1993).

  13. F. G. Shi, Scripta Metal, et Mater, (in press).

  14. F. G. Shi, unpublished research.

  15. D. Turnbull and M. H. Cohen, in Modern Aspects of the Vitreous State, edited by J. D. McKenzie (Butterworths, London, 1960), Vol. 1, Chap. 2; H. Yinnon and D. R. Uhlmann, J. Non-Cryst. Solids 50, 189 (1982); K.F. Kelton and A.L. Greer, J. Non-Cryst. Solids 79 (1986); Z. Kozisek, in Kinetic Phase Diagrams: Nonequilibrium Phase Transitions, edited by Z. Chvoj, J. Sestak, and A. Triska (Elsevier, New York, 1991).

  16. J. I. Frenkel, Kinetic Theory of Liquids (Clarendon, London, 1955), Chap. VI.

    Google Scholar 

  17. G. Shi, J.H. Seinfeld, and K. Okuyama, Phys. Rev. A 41, 2101 (1990); G. Shi and J. H. Seinfeld, J. Chem. Phys. 93, 9033 (1990); G. Shi and J. H. Seinfeld, J. Mater. Res. 6, 2091, 2097 (1991).

  18. F.G. Shi, Scripta Metal. Mater. 30, 1151 (1994); F.G. Shi and J. H. Seinfeld, Mater. Chem. and Phys. 37, 1 (1994); F. G. Shi and J.H. Seinfeld, AIChE J. 40, 11 (1994).

  19. F. G. Shi, Mater. Chem. Phys. (in press).

  20. F. G. Shi, Chem. Phys. Lett. 212, 421 (1993); Phys. Lett. A183, 311 (1993).

  21. F.G. Shi, Scripta Metal, et Mater. 30, 1195 (1994).

    Article  CAS  Google Scholar 

  22. J. J. Hoyt and G. Sundar, Scripta Metal, et Mater. 29, 1535 (1993).

    Article  Google Scholar 

  23. D. Turnbull and J. C. Fisher, J. Chem. Phys. 17, 71 (1949); E. G. Rowlands and P.F. James, Phys. Chem. Glasses 20, 1 (1979); J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10; S. R. Stiffler, P. V. Evans, and A. L. Greer, Acta Metal. Mater. 40, 1617 (1992).

  24. D.W. van Krevelen and P.J. Hoftyzer, Properties of Polymers (Elsevier, Amsterdam, 1976), p. 68.

    Google Scholar 

  25. See a good review by I. Gutzow, Contemp. Phys. 21, 243 (1980); also I. Gutzow, I. Avramov, and K. Kastener, J. Non-Cryst. Solids 7, 97 (1990).

  26. H. Vogel, Phys. Z. 22, 645 (1921); G. Tammann and G. Hesse, Z. Anorg. Allgem. Chem. 156, 245 (1926); D. Davidson and R. H. Cole, J. Chem. Phys. 19, 1484 (1951).

  27. R. Brtining and K. Samwer, Phys. Rev. B 46, 11318 (1992).

    Article  Google Scholar 

  28. C. T. Moynihan, A. J. Easteal, J. Wilder, and J. Tucker, J. Phys. Chem. 78, 2673 (1974); R. Luck, Q. Jiang, and B. Predel, J. Non-Cryst. Solids 117/118, 911 (1990).

  29. J. Baschnagel, K. Binder, and H.P. Wittmann, J. Phys. Cond. Matt. 5, 1597 (1993).

    Article  CAS  Google Scholar 

  30. H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); E. Garrone and L. Battezzati, Philos. Mag. B52, 1033 (1985).

  31. I. Gutzow and A. Dobreva, J. Non-Cryst. Solids 129, 266 (1991).

    Article  Google Scholar 

  32. C. Domb, J. Phys. A: Math. Gen. 9, 283 (1976).

    Article  Google Scholar 

  33. H. J. Fecht and W. L. Johnson, Nature 334, 50 (1988); J. L. Tallon, Nature 342, 658 (1989); W. L. Johnson, M. Li, and C. E. Krill III, J. Non-Cryst. Solids 156–158, 481 (1993).

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  1. Department of Chemical and Biochemical Engineering and Materials Science and Engineering Program, School of Engineering, University of California, California, 92717-2575, Irvine, USA

    Frank G. Shi

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Shi, F.G. Glass transition: A unified treatment. Journal of Materials Research 9, 1908–1916 (1994). https://doi.org/10.1557/JMR.1994.1908

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