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    (Old and New) Theories On The Glass Transition

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    Rawlinson
    The document discusses theories on the glass transition from both older and newer perspectives: [1] Older theories include free volume theory, Adam-Gibbs theory, and mode-coupling theory. [2] The energy landscape paradigm views the glass transition in terms of an underlying potential energy landscape. [3] Newer theories still under discussion include random first-order transition theory, spin glass theory, frustration-limited domains theory, and dynamical facilitation theory. However, the nature of the glass transition remains unclear with many competing theories proposed.

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    (Old and New) Theories On The Glass Transition

    Uploaded by

    Rawlinson
    35 views25 pages
    The document discusses theories on the glass transition from both older and newer perspectives: [1] Older theories include free volume theory, Adam-Gibbs theory, and mode-coupling theory. [2] The energy landscape paradigm views the glass transition in terms of an underlying potential energy landscape. [3] Newer theories still under discussion include random first-order transition theory, spin glass theory, frustration-limited domains theory, and dynamical facilitation theory. However, the nature of the glass transition remains unclear with many competing theories proposed.

    Original Description:

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    Original Title

    Course on Glasses-3b

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    The document discusses theories on the glass transition from both older and newer perspectives: [1] Older theories include free volume theory, Adam-Gibbs theory, and mode-coupling theory. [2] The energy landscape paradigm views the glass transition in terms of an underlying potential energy landscape. [3] Newer theories still under discussion include random first-order transition theory, spin glass theory, frustration-limited domains theory, and dynamical facilitation theory. However, the nature of the glass transition remains unclear with many competing theories proposed.

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    35 views25 pages

    (Old and New) Theories On The Glass Transition

    Uploaded by

    Rawlinson
    The document discusses theories on the glass transition from both older and newer perspectives: [1] Older theories include free volume theory, Adam-Gibbs theory, and mode-coupling theory. [2] The energy landscape paradigm views the glass transition in terms of an underlying potential energy landscape. [3] Newer theories still under discussion include random first-order transition theory, spin glass theory, frustration-limited domains theory, and dynamical facilitation theory. However, the nature of the glass transition remains unclear with many competing theories proposed.

    Copyright:

    © All Rights Reserved
    Download as PPT, PDF, TXT or read online from Scribd
    Download as ppt, pdf, or txt
    of 25

    3.

    THE GLASS STATE AND THE GLASS TRANSITION:


    THERMODYNAMIC and KINETIC ASPECTS

    (old and new) theories on the


    GLASS TRANSITION
    a) Old theories (but still being used) on the
    glass transition

    Free volume theory

    (Entropic) Adam & Gibbs theory

    Mode-coupling theory
    z *
    Average transition probability: W (T ) A exp
    k BT
    minimum size of the rearranging unit: z*

    * *
    s z
    c
    s k B ln 2
    *
    c
    Sc N

    1 B Nsc*
    exp B
    W (T ) TSc kB
    MODE-COUPLING THEORY:

    Ergodicity parameter k(t) is the Fourier transform


    of the van Hove density-density autocorrelation function
    G(r,t) = 1/ < (r,t) (0,0)>
    Critical point when c = 1:

    c < 1: lim t k(t) = 0 , liquid (ergodic)


    c > 1: lim t k(t) 0 , glass (non-ergodic)

    It predicts a power-law singularity of and :


    1.765

    1
    c
    Evolution of the self-intermediate scattering function for a supercooled Lennard-Jones
    binary mixture (molecular dynamics simulation for 1000 atoms).
    b) the ENERGY LANDSCAPE paradigm [Goldstein, 1969]
    ENTROPY
    c) New theories -under discussion- on the
    glass transition
    Present controversy:
    Does a glass possess a finite residual entropy at T=0?
    How does the entropy of a glass-forming system change
    in the glass transition range?
    Classical thermodynamic view
    [Nernst, Simon, Giauque; Gutzow&Schmeltzer, Goldstein]:
    YES, configuracional entropy of the supercooled liquid is frozen-in
    at T = Tg , S (Tg) = 0, giving S(0) 0.
    Entropy loss view
    [Gupta&Mauro, Kivelson&Reiss]:
    NO, laboratory glass transition is a non-spontaneous process from the
    ergodic (liquid) to a broken-ergodic (glass) state. The phase space of the
    glass is a small subset of that of the liquid. As a consequence there must
    be an entropy loss (without latent heat): S (Tg) > 0, but S(0) = 0.
    Classical thermodynamic view
    [Nernst, Simon, Giauque; Gutzow&Schmeltzer, Goldstein]:
    YES, configuracional entropy of the supercooled liquid is frozen-in
    at T = Tg , S (Tg) = 0, giving S(0) 0.

    J. Non-Cryst. Solids 355 (2009) 581-594


    Entropy loss view
    [Gupta&Mauro, Kivelson&Reiss]:
    NO, laboratory glass transition is a non-spontaneous process from the
    ergodic (liquid) to a broken-ergodic (glass) state. The phase space of the
    glass is a small subset of that of the liquid. As a consequence there must
    be an entropy loss (without latent heat): S (Tg) > 0, but S(0) = 0.

    J. Non-Cryst. Solids 355 (2009) 595-599


    c) New theories -under discussion- on the
    glass transition
    * Many competing recent theories
    - Random First Order Transition (mosaic theory) [Wolynes et al.]
    - Spin Glasses Theory : mean-field p-spin model [Moore]
    - Frustration-limited domains [Kivelson et al., Tarjus et al.]
    - Hierarchical Random Energy Model [Parisi]
    - Dynamical Facilitation Theory [Chandler and Garrahan]
    - Free-energy landscape theories
    - Two-temperature thermodynamic theory [Nieuwenhuizen]
    -
    F TS c (T ) R d YR ,
    d 1

    1
    1 d
    mosaic
    T Tk
    1
    1 d
    AG
    T Tk
    c) New theories -under discussion- on the
    glass transition

    The Nature of Glass Remains


    Anything but Clear

    (29. July. 2008)

    Mark Interrante

    ENIGMA Molten glass being worked into an ornament.


    Understanding glass could lead to better products
    and offer headway in other scientific problems.

    David A. Weitz, a physics professor at Harvard, joked,


    There are more theories of the glass transition than there
    are theorists who propose them.

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