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Glass transition: A unified treatment

Published online by Cambridge University Press:  03 March 2011

Frank G. Shi
Frank G. Shi
Affiliation:
Department of Chemical and Biochemical Engineering and Materials Science and Engineering Program, School of Engineering, University of California, Irvine, California 92717-2575
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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.

Type
Articles
Information
Journal of Materials Research , Volume 9 , Issue 7 , July 1994 , pp. 1908 - 1916
Copyright
Copyright © Materials Research Society 1994

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References

REFERENCES

1Elliott, S. R., Physics of Amorphous Materials (Longman Scientific & Technical and John Wiley & Sons Inc., New York, 1992), Chap. 2.Google Scholar
2Zallen, R., The Physics of Amorphous Solids (John Wiley & Sons, New York, 1983).Google Scholar
3Dynamic Aspects of Structural Change in Liquids and Glasses, edited by Angell, C. A. and Goldstein, M. (New York Academy of Science, New York, 1986).Google Scholar
4Kauzmann, W., Chem. Rev. 43, 219 (1948).CrossRefGoogle Scholar
5e.g., Kirkpatrick, T.R. and Wolynes, P.G., Phys. Rev. A35, 3072 (1987); Sethna, J.P., Europhys. Lett. 6, 529 (1988); Stein, D.L. and Palmer, R.G., Phys. Rev. B 38, 12035 (1988); Vilgid, T.A., Polym. Commun. 29, 327 (1988); Sethna, J. P., Shore, J. D., and Hung, M., Phys. Rev. B 44, 4943 (1991).CrossRefGoogle Scholar
6For a brief survey of the microscopic models, see Ref. 1.Google Scholar
7Gibbs, J. H. and DiMarzio, E.A., J. Chem. Phys. 28, 373 (1958); Adam, G. and Gibbs, J.H., J. Chem. Phys. 43, 139 (1965); Ngai, K.L., Rendell, R. W., and Plazek, D. J., J. Chem. Phys. 94, 3018 (1991).CrossRefGoogle Scholar
8Cohen, M. H. and Grest, G. S., J. Non-Cryst. Solids 61/62, 749 (1984); Cohen, M.H. and Turnbull, D., J. Chem. Phys. 34, 120 (1961); 52, 3038 (1970); Spaepen, F., in Physics of Defects, edited by Balian, R., Kleman, M., and Poirier, J-P. (North-Holland, Amsterdam, 1981), p. 133.Google Scholar
9Leutheusser, E., Phys. Rev. A 29, 2765 (1984); Götze, W. and Sjögren, L., Rep. Prog. Phys. 55, 241 (1992); and references therein.CrossRefGoogle Scholar
10e.g., Elderfield, D. and Sherrington, D., J. Phys. C16, L497 LI169 (1983).Google Scholar
11e.g., Ramakrishnan, T. V. and Yussouff, M., Phys. Rev. B 19, 2775 (1979); Oxtoby, D. W., in Liquids, Freezing and Glass Transition, edited by Hansen, J. P., Levesque, D., and Zinn-Justin, J. (North-Holland, Amsterdam, 1991); see also a review by Haymet, A. D. J., Ann. Rep. Phys. Chem. 38, 89 (1987).Google Scholar
12e.g., Zwanzig, R., Kinam 3, (1981); Jöackle, J., Rep. Prog. Phys. 49, 171 (1986); Stillinger, F. H. and Root, L. J., J. Chem. Phys. 89, 5081 (1988); Deng, D., Argon, A. S., and Yip, S. L., Philos. Trans. Roy. Soc. A329, 595 (1989); Vandenbeukel, A. and Sietsma, J., Scripta Metall. et Mater. 38, 383 (1990); Scherer, G.W., J. Non-Cryst. Solids 123, 75 (1990); Mohanty, U., Physica A177, 345 (1991); Lewis, J., Phys. Rev. B 44, 4245 (1991); Bendler, J. T. and Shlesinger, M. F., J. Phys. Chem. 96, 3970 (1992); Edwards, S. F., Int. J. Mod. Phys. B6, 1587 (1992); Roland, C. M. and Ngal, K. L., Macromolec. 25, 5765 (1992); Kob, W. and Andersen, H. C., Phys. Rev. E47, 3281 (1993); Lewis, L.J. and Wahnstrom, G., Solid State Commun. 86, 295 (1993); Johari, G.P., J. Chem. Phys. 98, 7324 (1993); Hunt, A., J. Non-Cryst. Solids 160, 183 (1993); Dattagupta, S. and Turski, L.A., Phys. Rev. E47, 1222 (1993); Vilgis, T.A., Phys. Rev. bf B47, 2882 (1993); Bohmer, R., Ngai, K. L., Angell, C. A., and Plazek, D. J., J. Chem. Phys. 48, 4201 (1993).Google Scholar
13Shi, F. G., Scripta Metal, et Mater, (in press).Google Scholar
14Shi, F. G., unpublished research.Google Scholar
15Turnbull, D. and Cohen, M. H., in Modern Aspects of the Vitreous State, edited by McKenzie, J. D. (Butterworths, London, 1960), Vol. 1, Chap. 2; Yinnon, H. and Uhlmann, D. R., J. Non-Cryst. Solids 50, 189 (1982); Kelton, K.F. and Greer, A.L., J. Non-Cryst. Solids 79 (1986); Kozisek, Z., in Kinetic Phase Diagrams: Nonequilibrium Phase Transitions, edited by Chvoj, Z., Sestak, J., and Triska, A. (Elsevier, New York, 1991).Google Scholar
16Frenkel, J. I., Kinetic Theory of Liquids (Clarendon, London, 1955), Chap. VI.Google Scholar
17Shi, G., Seinfeld, J. H., and Okuyama, K., Phys. Rev. A 41, 2101 (1990); Shi, G. and Seinfeld, J. H., J. Chem. Phys. 93, 9033 (1990); Shi, G. and Seinfeld, J. H., J. Mater. Res. 6, 2091, 2097 (1991).Google Scholar
18Shi, F. G., Scripta Metal. Mater. 30, 1151 (1994); Shi, F.G. and Seinfeld, J. H., Mater. Chem. and Phys. 37, 1 (1994); Shi, F. G. and Seinfeld, J.H., AIChE J. 40, 11 (1994).CrossRefGoogle Scholar
19Shi, F. G., Mater. Chem. Phys. (in press).Google Scholar
20Shi, F. G., Chem. Phys. Lett. 212, 421 (1993); Phys. Lett. A183, 311 (1993).Google Scholar
21Shi, F. G., Scripta Metal, et Mater. 30, 1195 (1994).CrossRefGoogle Scholar
22Hoyt, J. J. and Sundar, G., Scripta Metal, et Mater. 29, 1535 (1993).CrossRefGoogle Scholar
23Turnbull, D. and Fisher, J. C., J. Chem. Phys. 17, 71 (1949); Rowlands, E. G. and James, P.F., Phys. Chem. Glasses 20, 1 (1979); Christian, J. W., The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10; Stiffler, S. R., Evans, P. V., and Greer, A. L., Acta Metal. Mater. 40, 1617 (1992).CrossRefGoogle Scholar
24van Krevelen, D. W. and Hoftyzer, P. J., Properties of Polymers (Elsevier, Amsterdam, 1976), p. 68.Google Scholar
25See a good review by Gutzow, I., Contemp. Phys. 21, 243 (1980); also Gutzow, I., Avramov, I., and Kästener, K., J. Non-Cryst. Solids 7, 97 (1990).Google Scholar
26Vogel, H., Phys. Z. 22, 645 (1921); Tammann, G. and Hesse, G., Z. Anorg. Allgem. Chem. 156, 245 (1926); Davidson, D. and Cole, R. H., J. Chem. Phys. 19, 1484 (1951).Google Scholar
27Brüning, R. and Samwer, K., Phys. Rev. B 46, 11318 (1992).CrossRefGoogle Scholar
28Moynihan, C. T., Easteal, A. J., Wilder, J., and Tucker, J., J. Phys. Chem. 78, 2673 (1974); Lück, R., Jiang, Q., and Predel, B., J. Non-Cryst. Solids 117/118, 911 (1990).CrossRefGoogle Scholar
29Baschnagel, J., Binder, K., and Wittmann, H. P., J. Phys. Cond. Matt. 5, 1597 (1993).Google Scholar
30Chen, H. S. and Turnbull, D., J. Chem. Phys. 48, 2560 (1968); Garrone, E. and Battezzati, L., Philos. Mag. B52, 1033 (1985).CrossRefGoogle Scholar
31Gutzow, I. and Dobreva, A., J. Non-Cryst. Solids 129, 266 (1991).CrossRefGoogle Scholar
32Domb, C., J. Phys. A: Math. Gen. 9, 283 (1976).Google Scholar
33Fecht, H. J. and Johnson, W. L., Nature 334, 50 (1988); Tallon, J. L., Nature 342, 658 (1989); Johnson, W. L., Li, M., and Krill, C. E. III, J. Non-Cryst. Solids 156–158, 481 (1993).CrossRefGoogle Scholar