Dynamics and thermodynamics of the glass transition

doi:10.1103/PHYSREVE.73.0

Title: Dynamics and thermodynamics of the glass transition

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Abstract

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature T{sub K}. This partially broken ergodicity seems to explain the vanishing entropy at T{sub K} and other observed relations between dynamics and thermodynamics at the glass transition.

Authors:

Langer, J.S. ^[1]

Department of Physics, University of California, Santa Barbara, California 93106-9530 (United States)

Publication Date:: Sat Apr 15 00:00:00 EDT 2006

OSTI Identifier:: 20779238

Resource Type:: Journal Article

Resource Relation:: Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.73.041504; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; ENTROPY; EXCITATION; FLUCTUATIONS; GLASS; MOLECULAR STRUCTURE; PHASE TRANSFORMATIONS; RELAXATION; THERMODYNAMICS

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                    Langer, J.S. Dynamics and thermodynamics of the glass transition.  United States: N. p., 2006. 
        Web.  doi:10.1103/PHYSREVE.73.0.

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                    Langer, J.S. Dynamics and thermodynamics of the glass transition.  United States.  doi:10.1103/PHYSREVE.73.0.

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                    Langer, J.S. Sat .  
        "Dynamics and thermodynamics of the glass transition".  United States.  
        doi:10.1103/PHYSREVE.73.0.

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@article{osti_20779238,

  title        = {Dynamics and thermodynamics of the glass transition},

  author       = {Langer, J.S.},

  abstractNote = {The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature T{sub K}. This partially broken ergodicity seems to explain the vanishing entropy at T{sub K} and other observed relations between dynamics and thermodynamics at the glass transition.},

  doi          = {10.1103/PHYSREVE.73.0},

  journal      = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

  number       = 4,

  volume       = 73,

  place        = {United States},

  year         = {Sat Apr 15 00:00:00 EDT 2006},

  month        = {Sat Apr 15 00:00:00 EDT 2006}

}

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DOI: 10.1103/PHYSREVE.73.0

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