Skip to main content
SpringerLink
Log in

Relaxation time and cooling rate of a liquid in the glass transition range

  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

The transfer of kinetic units (atoms or groups of atoms) in amorphous materials from one quasiequilibrium position to another quasi-equilibrium position is governed by the fluctuations of both the energy and the entropy of the system. In the glass transition range of liquids, the entropy mechanism plays a dominant role: fluctuations of the particle packing appear to be more significant than the accumulation of the energy. At high temperatures above the glass transition range, the energy mechanism plays a decisive role. The physical meaning of the parameter involved in the Bartenev equation relating the relaxation time to the cooling rate at the glass transition temperature is discussed. A technique is proposed for calculating this parameter with allowance made for the temperature dependence of the activation energy in the liquid-glass transition range. A variant of the modification of this equation is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sanditov, D.S. and Bartenev, G.M., Fizicheskie svoistva neuporyadochennykh struktur (The Physical Properties of Disordered Structures), Novosibirsk: Nauka, 1982 [in Russian].

    Google Scholar 

  2. Mazurin, O.V., Steklovanie (Glass Transition), Leningrad: Nauka, 1986 [in Russian].

    Google Scholar 

  3. Rostiashvili, V.G., Irzhak, V.I., and Rozenberg, B.A., Steklovanie polimerov (Glass Transition in Polymers), Leningrad: Khimiya, 1987 [in Russian].

    Google Scholar 

  4. Vol’kenshtein, M.V. and Ptitsyn, O.B., Relaxation Theory of the Glass Transition, Dokl. Akad. Nauk SSSR, 1955, vol. 103, no. 5, pp. 795–798.

    CAS  Google Scholar 

  5. Bartenev, G.M. and Luk’yanov, I.A., Dependence of the Glass Transition Temperature on the Heating Rate for Amorphous Materials and the Relation of the Glass Transition Temperature to the Activation Energy, Zh. Fiz. Khim., 1955, vol. 29, no. 8, pp. 1486–1498.

    CAS  Google Scholar 

  6. Bartenev, G.M. and Lomovskoi, V.A., Molecular Mechanisms of Vitrification of Inorganic Glasses, Zh. Fiz. Khim., 2003, vol. 77, no. 12, pp. 2266–2276 [Russ. J. Phys. Chem. (Engl. transl.), 2003, vol. 77, no. 12, pp. 2045–2054].

    CAS  Google Scholar 

  7. Bartenev, G.M. and Barteneva, A.G., Relaksatsionnye svoistva polimerov (Relaxation Properties of Polymers), Moscow: Khimiya, 1992 [in Russian].

    Google Scholar 

  8. Tool, A.Q., Relaxation between Inelastic Deformation and Thermal Expansion of Glass in Its Annealing Range, J. Am. Ceram. Soc., 1946, vol. 29, no. 9, pp. 240–253.

    Article  CAS  Google Scholar 

  9. Naraynaswamy, O.S., Model of Structural Relaxation in Glass, J. Phys. Chem., 1971, vol. 54, no. 10, pp. 491–498.

    Google Scholar 

  10. Moynihan, C.T., Easteal, A.J., Wilder, J., and Ticker, J., Dependence of the Glass Transition Temperature on Heating and Cooling Rate, J. Phys. Chem., 1974, vol. 78, no. 26, pp. 2673–2677.

    Article  CAS  Google Scholar 

  11. Olemskoi, A.I. and Khomenko, A.V., The Synergetic Theory of the Glass Transition in Liquids, Zh. Tekh. Fiz., 2000, vol. 70, no. 6, pp. 10–13 [Tech. Phys. (Engl. transl.), 2000, vol. 70, no. 6, pp. 677–682].

    Google Scholar 

  12. Priven, A.I., Calculation of Temperature Dependences of the Viscosity and Volume Relaxation Time for Oxide Glass-Forming Melts from Chemical Composition and Dilatometric Glass Transition Temperature, Fiz. Khim. Stekla, 2001, vol. 27, no. 6, pp. 772–793 [Glass Phys. Chem. (Engl. transl.), 2001, vol. 27, no. 6, pp. 527–542].

    Google Scholar 

  13. Frenkel, Ya.I., Kineticheskaya teoriya zhidkostei (The Kinetic Theory of Liquids), Leningrad: Nauka, 1975 [in Russian].

    Google Scholar 

  14. Glasstone, S., Laidler, K., and Eyring, H., The Theory of Rate Processes, New York: Princeton University Press, 1941. Translated under the title Teoriya absolyutnykh skorostei reaktsii, Moscow: Inostrannaya Literatura, 1948.

    Google Scholar 

  15. Cohen, M.H. and Turnbull, D., Molecular Transport in Liquids and Glasses, J. Chem. Phys., 1959, vol. 31, no. 5, pp. 1164–1169.

    Article  CAS  Google Scholar 

  16. Sanditov, D.S., Entropy of Activation of Atomic Excitation near the Glass Transition, Dokl. Akad. Nauk, 2005, vol. 403, no. 4, pp. 213–217 [Dokl. Phys. Chem. (Engl. transl.), 2005, vol. 403, no. 4, pp. 146–149].

    Google Scholar 

  17. Burshtein, A.I., On the Origin of the Pseudoactivation Temperature Dependence of the Viscosity, Dokl. Akad. Nauk SSSR, 1973, vol. 213, no. 5, pp. 1109–1112.

    Google Scholar 

  18. Macedo, P.B. and Litovitz, T.A., On the Relative Roles of Free Volume and Activation Energy in the Viscosity of Liquids, J. Chem. Phys., 1965, vol. 42, no. 1, pp. 245–256.

    Article  CAS  Google Scholar 

  19. Sanditov, D.S., Toward the Theory of Molecular Mobility in Liquids and Glasses over Wide Ranges of Temperatures and Pressures, Izv. Vyssh. Uchebn. Zaved., Fiz., 1971, no. 2, pp. 17–23.

  20. Matsuoka, S., Aloisio, C.J., and Bair, H.E., The Temperature Drop in Glassy Polymers during Deformation, J. Appl. Phys., 1977, vol. 48, no. 10, pp. 4058–4062.

    Article  CAS  Google Scholar 

  21. Sanditov, D.S., Condition of Glass Transition in Liquids and Lindemann’s Criterion for Melting in the Excited Atom Model, Dokl. Akad. Nauk, 2003, vol. 390, no. 2, pp. 209–213 [Dokl. Phys. Chem. (Engl. transl.), 2003, vol. 390, no. 2, pp. 122–125].

    Google Scholar 

  22. Sanditov, D.S., The Model of Excited Atoms and Viscoelastic Properties of Polymers and Glasses, Vysokomol. Soedin., Ser. A, 2005, vol. 47, no. 3, pp. 478–489 [Polym. Sci., Ser. A (Engl. transl.), 2005, vol. 47, no. 3, pp. 289–298].

    CAS  Google Scholar 

  23. Sanditov, D.S. and Bainova, A.B., Viscous Flow and Plastic Deformation of Glasses in the Model of Excited Atoms, Fiz. Khim. Stekla, 2004, vol. 30, no. 2, pp. 153–177 [Glass Phys. Chem. (Engl. transl.), 2004, vol. 30, no. 2, pp. 113–131].

    Google Scholar 

  24. Adam, G. and Gibbs, J.H., On Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids, J. Chem. Phys., 1965, vol. 43, no. 1, pp. 139–146.

    Article  CAS  Google Scholar 

  25. Nemilov, S.V., Viscous Flow of Glasses in Relation to Their Structure: Application of the Theory of Rate Processes, Fiz. Khim. Stekla, 1992, vol. 18, no. 1, pp. 3–44 [Sov. J. Glass Phys. Chem. (Engl. transl.), 1992, vol. 18, no. 1, pp. 1–21].

    CAS  Google Scholar 

  26. Nemilov, S.V., Thermodynamic and Kinetic Aspects of the Vitreous State, Boca Raton: CRC, 1995.

    Google Scholar 

  27. Ferry, J.D., Visco-Elastic Properties of Polymers, New York: Wiley, 1961. Translated under the title Vyazkouprugie svoistva polimerov, Moscow: Inostrannaya Literatura, 1963.

    Google Scholar 

  28. Durov, V.A. and Shakhparonov, M.I., The Theory of Collective Reactions in Liquid Phases: VI. The Williams-Landell-Ferry Equation, Zh. Fiz. Khim., 1979, vol. 53, no. 10, pp. 2456–2459.

    CAS  Google Scholar 

  29. Mazurin, O.V., Strel’tsina, M.V., and Shvaiko-Shvaikovskaya, T.P., Svoistva stekol i stekloobrazuyushchikh rasplavov. Spravochnik (Properties of Glasses and Glass-Forming Melts: A Handbook), Leningrad: Nauka, vol. 1, 1977 [in Russian].

    Google Scholar 

  30. Sudzuki, K., Fudzimori, H., and Hasimoto, K., Amorphous Metals, Moscow: Metallurgiya, 1987 [in Russian].

    Google Scholar 

  31. Bornhoft, H. and Bruckner, R., Elastic and Inelastic Properties of Soda-Lime-Silicate Melts, Glass Sci. Technol. (Frankfurt/Main), 1999, vol. 72, no. 10, pp. 315–321.

    CAS  Google Scholar 

  32. Mel’nichenko, T.D., Rizak, V.M., Mel’nichenko, T.N., and Fedelesh, V.I., Parameters of the Fluctuation Free Volume Theory for Glasses in the Ge-As-Se System, Fiz. Khim. Stekla, 2004, vol. 30, no. 5, pp. 553–564 [Glass Phys. Chem. (Engl. transl.), 2004, vol. 30, no. 5, pp. 406–414].

    Google Scholar 

  33. Sanditov, D.S. and Kozlov, G.V., On the Nature of Correlation between the Elastic Constants and Glass Transition Temperature of Amorphous Polymers, Fiz. Khim. Stekla, 1993, vol. 19, no. 4, pp. 561–571 [Glass Phys. Chem. (Engl. transl.), 1993, vol. 19, no. 4, pp. 289–294].

    CAS  Google Scholar 

  34. Sanditov, D.S., Sangadiev, S.Sh., and Kozlov, G.V., On the Correlation between the Elastic Modulus of Vitreous Solids and the Glass Transition Temperature of Melts, Fiz. Khim. Stekla, 1998, vol. 24, no. 6, pp. 758–766 [Glass Phys. Chem. (Engl. transl.), 1998, vol. 24, no. 6, pp. 539–545].

    Google Scholar 

  35. Mazurin, O.V. and Klyuev, V.P., Dilatometric Investigation of the Structural Hysteresis in Some Multicomponent Glasses, Fiz. Khim. Stekla, 1975, vol. 1, no. 3, pp. 245–250.

    CAS  Google Scholar 

  36. Klyuev, V.P. and Bulaeva, A.V., Viscosity and Thermal Expansion of Lead Borate Glasses in the Glass Transition Range, Fiz. Khim. Stekla, 1980, vol. 6, no. 6, pp. 674–678.

    CAS  Google Scholar 

  37. Mazurin, O.V. and Stolyar, S.V., On the Relationship between the Glass Transition and the Liquidus Temperatures for Some Eutectic Compositions in the Sodium Borosilicate System, Fiz. Khim. Stekla, 1984, vol. 10, no. 2, pp. 163–166.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Buryat State University, ul. Smolina 24a, Ulan-Ude, 670000, Russia

    B. D. Sanditov & S. Sh. Sangadiev

  2. Department of Physical Problems, Buryat Research Center, Siberian Division, Russian Academy of Sciences, ul. Sakh’yanovoi 8, Ulan-Ude, 670047, Russia

    D. S. Sanditov

Authors
  1. B. D. Sanditov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Sh. Sangadiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. S. Sanditov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. D. Sanditov.

Additional information

Original Russian Text © B.D. Sanditov, S.Sh. Sangadiev, D.S. Sanditov, 2007, published in Fizika i Khimiya Stekla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sanditov, B.D., Sangadiev, S.S. & Sanditov, D.S. Relaxation time and cooling rate of a liquid in the glass transition range. Glass Phys Chem 33, 445–454 (2007). https://doi.org/10.1134/S1087659607050021

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1087659607050021

Keywords

Search

Navigation