(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 There is no such a thing as “the theory on the glass transition”…

Free volume

After complicated statistical models and calculations, it predicted a first-order transition of a percolative type. It does not work really! Only the free volume concept is useful.

Now configurational ENTROPY is the supposed order parameter… It relates the relaxation time (for cooperatively rearranging regions through thermal activated processes) to the configurational entropy. Analytic simplification…. We obtain the phenomenological VTF equation !!!

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

Tk (S) and To (kinetic) would be the same… it anticipates the hypothesis of an ideal thermodynamic transition at T=Tk

Mas recientemente, MCT es una variante de la Tª hidrodinamica de liquidos simples Ec integro-diferencial, con acoplamiento de modos, etc. Para un valor critico de lambda, el sistema pasa de ergodico a no ergodico (la f. de correlacion pasa de tender a 0 para t->infinito a una constante)

En breve, describe muy bien la dinamica de los liquidos sobrenfriados por encima de Tg, pero no el estado vitreo. Idealmente hay una transicion dinamica a Tc (20% mayor que Tg) donde divergerian los tiempos de relajacion…

binary mixture (molecular dynamics simulation for 1000 atoms). Comparaciones con simulaciones de ordenador en el estado liquido. Escenario correcto de dos “plataformas” en el SCL 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] Mas que una teoria, un paradigma o escenario Proyeccion en 2-D de una hipersuperficie de la energia potencial de 3N+1 dimensiones…

Ilustrativa descripcion de cinetica y Termodin Ilustrativa descripcion de cinetica y Termodin. con el paisaje de energias ENTROPY

Does a glass possess a finite residual entropy at T=0? 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 transiion 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. en las ultimos 20 años ha renacido el interes de los teoricos por explicar la transicion vitrea… Incluso muy recientemente ha surgido una polemica sobre un concepto tan basico y aparentemente admitido como que los vidrios tienen en efecto una entropia “residual” distinta de cero a T=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

[Gupta&Mauro, Kivelson&Reiss]: 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 … 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] … por citar sólo las más conocidas

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.” El año pasado, reportaje en el NYT muchos teóricos (americanos) aportaron su visión dispar sobre la debatida transicoon vitrea Se citaba el comentario de uno de ellos, David Weitz…