Free volume theory (Entropic) Adam & Gibbs theory Mode-coupling theory

1. 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

5. Average transition probability: minimum size of the rearranging unit: z* 

10. 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  :

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

13. b) the ENERGY LANDSCAPE paradigm[Goldstein, 1969]

14. ENTROPY

16. 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.

17. 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

18. 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

19. 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] • …

23. 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.”