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Enthalpy landscapes and the glass transition

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Scientific Modeling and Simulation SMNS

Abstract

A fundamental understanding of the glass transition is essential for enabling future breakthroughs in glass science and technology. In this paper, we review recent advances in the modeling of glass transition range behavior based on the enthalpy landscape approach. We also give an overview of new simulation techniques for implementation of enthalpy landscape models, including techniques for mapping the landscape and computing the long-time dynamics of the system. When combined with these new computational techniques, the enthalpy landscape approach can provide for the predictive modeling of glass transition and relaxation behavior on a laboratory time scale. We also discuss new insights from the enthalpy landscape approach into the nature of the supercooled liquid and glassy states. In particular, the enthalpy landscape approach provides for natural resolutions of both the Kauzmann paradox and the question of residual entropy of glass at absolute zero. We further show that the glassy state cannot be described in terms of a mixture of equilibrium liquid states, indicating that there is no microscopic basis for the concept of a fictive temperature distribution and that the glass and liquid are two fundamentally different states. We also discuss the connection between supercooled liquid fragility and the ideal glass transition.

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References

  1. Tait H.: Five Thousand Years of Glass. British Museum Press, London (1991)

    Google Scholar 

  2. Zanotto E.D., Gupta P.K.: Do cathedral glasses flow?—additional remarks. Am. J. Phys. 67(3), 260–262 (1999)

    Article  ADS  CAS  Google Scholar 

  3. Gupta P.K., Mauro J.C.: The laboratory glass transition. J. Chem. Phys. 126(22), 224504 (2007)

    Article  PubMed  ADS  Google Scholar 

  4. Tool A.Q.: Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29(9), 240–253 (1946)

    Article  CAS  Google Scholar 

  5. Narayanaswamy O.S.: A model of structural relaxation in glass. J. Am. Ceram. Soc. 54(10), 491–498 (1971)

    Article  CAS  Google Scholar 

  6. Turnbull D., Cohen M.H.: On the free-volume model of the liquid-glass transition. J. Chem. Phys. 52(6), 3038–3041 (1970)

    Article  ADS  Google Scholar 

  7. Cohen M.H., Grest G.S.: Liquid-glass transition, a free-volume approach. Phys. Rev. B 20(3), 1077–1098 (1979)

    Article  ADS  CAS  Google Scholar 

  8. Gupta P.K.: Models of the glass transition. Rev. Solid State Sci. 3(3–4), 221–257 (1989)

    Google Scholar 

  9. Gibbs J.H., DiMarzio E.A.: Nature of the glass transition and the glassy state. J. Chem. Phys. 28(3), 373–383 (1958)

    Article  ADS  CAS  Google Scholar 

  10. Leutheusser E.: Dynamical model of the liquid-glass transition. Phys. Rev. A 29(5), 2765–2773 (1984)

    Article  ADS  CAS  Google Scholar 

  11. Bengtzelius U., Götze W., Sjölander A.: Dynamics of supercooled liquids and the glass transition. J. Phys. C: Solid State Phys. 17(33), 5915–5934 (1984)

    Article  ADS  CAS  Google Scholar 

  12. Debenedetti P.G.: Metastable Liquids: Concepts and Principles. Princeton University, Princeton (1996)

    Google Scholar 

  13. Kob W.: Computer simulation of supercooled liquids and glasses. J. Phys.: Condens. Matter 11(10), R85–R115 (1999)

    Article  ADS  CAS  Google Scholar 

  14. Scherer G.W.: Relaxation in Glass and Composites. Wiley, New York (1986)

    Google Scholar 

  15. Jäckle J.: Models of the glass transition. Rep. Prog. Phys. 49(2), 171–231 (1986)

    Article  ADS  Google Scholar 

  16. Varshneya A.K.: Fundamentals of Inorganic Glasses, 2nd edn. Society of Glass Technology, Sunderland (2007)

    Google Scholar 

  17. Gupta P.K.: Non-crystalline solids: glasses and amorphous solids. J. Non-Cryst. Solids 195(1–2), 158–164 (1996)

    Article  ADS  CAS  Google Scholar 

  18. Goldstein M.: Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 51(9), 3728–3739 (1969)

    Article  ADS  CAS  Google Scholar 

  19. Stillinger F.H., Weber T.A.: Hidden structure in liquids. Phys. Rev. A 25(2), 978–989 (1982)

    Article  ADS  CAS  Google Scholar 

  20. Stillinger F.H., Weber T.A.: Dynamics of structural transitions in liquids. Phys. Rev. A 28(4), 2408–2416 (1983)

    Article  ADS  CAS  Google Scholar 

  21. Stillinger F.H.: Supercooled liquids, glass transitions, and the Kauzmann paradox. J. Chem. Phys. 88(12), 7818–7825 (1988)

    Article  ADS  CAS  MathSciNet  Google Scholar 

  22. Debenedetti P.G., Stillinger F.H., Truskett T.M., Roberts C.J.: The equation of state of an energy landscape. J. Phys. Chem. B 103(35), 7390–7397 (1999)

    Article  CAS  Google Scholar 

  23. Debenedetti P.G., Stillinger F.H.: Supercooled liquids and the glass transition. Nature 410(6825), 259–267 (2001)

    Article  PubMed  ADS  CAS  Google Scholar 

  24. Stillinger F.H., Debenedetti P.G.: Energy landscape diversity and supercooled liquid properties. J. Chem. Phys. 116(8), 3353–3361 (2002)

    Article  ADS  CAS  Google Scholar 

  25. Massen C.P., Doye J.P.K.: Power-law distributions for the areas of the basins of attraction on a potential energy landscape. Phys. Rev. E 75, 037101 (2007)

    Article  ADS  Google Scholar 

  26. Mauro J.C., Varshneya A.K.: A nonequilibrium statistical mechanical model of structural relaxation in glass. J. Am. Ceram. Soc. 89(3), 1091–1094 (2006)

    Article  CAS  Google Scholar 

  27. Zwanzig R.: Nonequilibrium Statistical Mechanics. Oxford University, New York (2001)

    Google Scholar 

  28. Mauro J.C., Loucks R.J., Gupta P.K.: Metabasin approach for computing the master equation dynamics of systems with broken ergodicity. J. Phys. Chem. A 111, 7957–7965 (2007)

    Article  PubMed  CAS  Google Scholar 

  29. Wales D.J.: Energy Landscapes. Cambridge University, Cambridge (2003)

    Google Scholar 

  30. Middleton T.F., Wales D.J.: Energy landscapes of model glasses. II. Results for constant pressure. J. Chem. Phys. 118(10), 4583–4593 (2003)

    Article  ADS  CAS  Google Scholar 

  31. Mauro J.C., Loucks R.J., Balakrishnan J.: Split-step eigenvector-following technique for exploring enthalpy landscapes at absolute zero. J. Phys. Chem. B 110(10), 5005–5011 (2006)

    Article  PubMed  CAS  Google Scholar 

  32. Mauro J.C., Loucks R.J., Balakrishnan J.: A simplified eigenvector-following technique for locating transition points in an energy landscape. J. Phys. Chem. A 109(42), 9578–9583 (2005)

    Article  PubMed  CAS  Google Scholar 

  33. Wang F., Landau D.P.: Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. Phys. Rev. E 64, 056101 (2001)

    Article  ADS  CAS  Google Scholar 

  34. Mauro J.C., Loucks R.J., Balakrishnan J., Raghavan S.: Monte Carlo method for computing density of states and quench probability of potential energy and enthalpy landscapes. J. Chem. Phys. 126, 194103 (2007)

    Article  PubMed  ADS  Google Scholar 

  35. Mauro J.C., Loucks R.J.: Selenium glass transition: a model based on the enthalpy landscape approach and nonequilibrium statistical mechanics. Phys. Rev. B 76, 174202 (2007)

    Article  ADS  Google Scholar 

  36. Moynihan C.T., Easteal A.J., DeBolt M.A., Tucker J.: Dependence of the fictive temperature of glass on cooling rate. J. Am. Ceram. Soc. 59(1–2), 12–16 (1976)

    Article  CAS  Google Scholar 

  37. Mauro J.C., Varshneya A.K.: Model interaction potentials for selenium from ab initio molecular simulations. Phys. Rev. B 71, 214105 (2005)

    Article  ADS  Google Scholar 

  38. Sreeram A.N., Varshneya A.K., Swiler D.R.: Molar volume and elastic properties of multicomponent chalcogenide glasses. J. Non-Cryst. Solids 128(3), 294–309 (1991)

    Article  ADS  CAS  Google Scholar 

  39. Senapati U., Varshneya A.K.: Viscosity of chalcogenide glass-forming liquids: an anomaly in the ‘strong’ and ‘fragile’ classification. J. Non-Cryst. Solids 197(2–3), 210–218 (1996)

    Article  ADS  CAS  Google Scholar 

  40. Palmer R.G.: Broken ergodicity. Adv. Phys. 31(6), 669–735 (1982)

    Article  ADS  Google Scholar 

  41. Goldstein S., Lebowitz J.L.: On the (Boltzmann) entropy of non-equilibrium systems. Physica D 193(1–4), 53–66 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  42. Speedy R.J.: The entropy of glass. Mol. Phys. 80(5), 1105–1120 (1993)

    Article  ADS  CAS  Google Scholar 

  43. Jäckle J.: On the glass transition and the residual entropy of glasses. Philos. Mag. B 44(5), 533–545 (1981)

    Article  Google Scholar 

  44. Mauro J.C., Gupta P.K., Loucks R.J.: Continuously broken ergodicity. J. Chem. Phys. 126, 184511 (2007)

    Article  PubMed  ADS  Google Scholar 

  45. Lebowitz J.L.: Microscopic origins of irreversible macroscopic behavior. Physica A 263, 516–527 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  46. Lebowitz J.L.: Statistical mechanics: a selective review of two central issues. Rev. Mod. Phys. 71(2), S346–S357 (1999)

    Article  CAS  Google Scholar 

  47. Kivelson D., Reiss H.: Metastable systems in thermodynamics: consequences, role of constraints. J. Phys. Chem. B 103, 8337–8343 (1999)

    Article  CAS  Google Scholar 

  48. Angell C.A.: Spectroscopy simulation and scattering, and the medium range order problem in glass. J. Non-Cryst. Solids 73(1–3), 1–17 (1985)

    Article  ADS  CAS  Google Scholar 

  49. Angell C.A.: Structural instability and relaxation in liquid and glassy phases. J. Non-Cryst. Solids 102(1–3), 205–221 (1988)

    Article  ADS  CAS  Google Scholar 

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

    Article  Google Scholar 

  51. Angell C.A., Ngai K.L., McKenna G.B., McMillan P.F., Martin S.W.: Relaxation in glassforming liquids and amorphous solids. J. Appl. Phys. 88(6), 3113–3157 (2000)

    Article  ADS  CAS  Google Scholar 

  52. Angell C.A.: Liquid fragility and the glass transition in water and aqueous solutions. Chem. Rev. 102, 2627–2650 (2002)

    Article  PubMed  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  54. Huang D., Simon S.L., McKenna G.B.: Equilibrium heat capacity of the glass-forming poly (α-methyl styrene) far below the Kauzmann temperature: the case of the missing glass transition. J. Chem. Phys. 119(7), 3590–3593 (2003)

    Article  ADS  CAS  Google Scholar 

  55. Stillinger F.H., Debenedetti P.G., Truskett T.M.: The Kauzmann paradox revisited. J. Phys. Chem. B 105(47), 11809–11816 (2001)

    Article  CAS  Google Scholar 

  56. Stillinger F.H., Debenedetti P.G.: Phase transitions, Kauzmann curves, and inverse melting. Biophys. Chem. 105(2), 211–220 (2003)

    Article  PubMed  CAS  Google Scholar 

  57. Tool A.Q., Eichlin C.G.: Variations caused in the heating curves of glass by heat treatment. J. Am. Ceram. Soc. 14, 276–308 (1931)

    Article  CAS  Google Scholar 

  58. Ritland H.N.: Limitations of the fictive temperature concept. J. Am. Ceram. Soc. 39(12), 403–406 (1956)

    Article  CAS  Google Scholar 

  59. Giovambattista N., Stanley H.E., Sciortino F.: Cooling rate, heating rate, and aging effects in glassy water. Phys. Rev. E 69, 050201(R) (2004)

    Article  ADS  Google Scholar 

  60. Lubchenko V., Wolynes P.G.: Theory of aging in structural glasses. J. Chem. Phys. 121(7), 2852–2865 (2004)

    Article  PubMed  ADS  CAS  Google Scholar 

  61. Mauro, J.C., Loucks, R.J., Gupta, P.K.: Fictive temperature and the glassy state. Phys. Rev. E. (2008, submitted)

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Authors and Affiliations

  1. Science and Technology Division, Corning Incorporated, Corning, NY, 14831, USA

    John C. Mauro

  2. Department of Physics and Astronomy, Alfred University, Alfred, NY, 14802, USA

    Roger J. Loucks

  3. New York State College of Ceramics, Alfred University, Alfred, NY, 14802, USA

    Arun K. Varshneya

  4. Department of Materials Science and Engineering, Ohio State University, Columbus, OH, 43210, USA

    Prabhat K. Gupta

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  1. John C. Mauro
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  2. Roger J. Loucks
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  4. Prabhat K. Gupta
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Correspondence to John C. Mauro.

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In loving memory of Salvatore M. Mauro. “Give a man a fish and he will eat for a day. Teach him how to fish and he will eat for a lifetime.”

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Mauro, J.C., Loucks, R.J., Varshneya, A.K. et al. Enthalpy landscapes and the glass transition. Sci Model Simul 15, 241–281 (2008). https://doi.org/10.1007/s10820-008-9092-2

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