• Free volume theory

• (Entropic) Adam & Gibbs theory

• Mode-coupling theory

(old and new) theories on theGLASS TRANSITION

a) “Old” theories (but still being used) on the glass transition

3. THE GLASS STATE AND THE GLASS TRANSITION:THERMODYNAMIC and KINETIC ASPECTS

Average transition probability:

Tk

zATW

B

*exp)(

minimum size of the rearranging unit: z*

N

z

S

s

c

c**

2ln*Bc ks

cTS

B

TWexp

)(

1 B

c

k

NsB

*

MODE-COUPLING THEORY:

Ergodicity parameter k(t) is the Fourier transformof 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)

765.1

1

c

It predicts a power-law singularity of and :

Evolution of the self-intermediate scattering function for a supercooled Lennard-Jonesbinary mixture (molecular dynamics simulation for 1000 atoms).

b) the ENERGY LANDSCAPE paradigm [Goldstein, 1969]

EN

TR

OP

Y

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

* 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] - …

c) “New” theories -under discussion- on the glass transition

1

,)(

d

YRRTTSF dc

d

kmosaic TT

1

1

d

kAG TT

1

1

The Nature of Glass RemainsAnything but Clear

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 thereare theorists who propose them.”

(29. July. 2008)

c) “New” theories -under discussion- on the glass transition