Jean-Pierre Hansen, Professeur Emerite de l’ENS Lyon et de l’Université de Cambridge, présentera un séminaire le jeudi 18 décembre 2014 à 14h dans la bibliothèque du laboratoire PHENIX (7e étage, bâtiment F, porte 754) intitulé :
Can equilibrium statistical mechanics provide a clue to the structural transition from a supercooled liquid to an « ideal » glass ?
Résumé
Supercooled liquids and glasses are out-of-equilibrium states which can be reached if crystal nuceation is avoided, e.g. by rapid quenching. Recent theories conjecture that the non-equilibrium glass transition is driven by an underlying equilibrium transition between a deeply supercooled liquid phase and an « ideal » glass phase in the limit of infinitely slow structural relaxation. We investigate this « random first order transition » (RFOT) by considering two weakly coupled replicae of a system of « soft spheres ». The structure and thermodynamics of this symmetric binary system are calculated using standard integral équations from the theory of liquids. We show that in the limit of vanishing inter-replica coupling, three thermodynamic branches may be mapped out as functions of temperature T well below the freezing temperature : a supercooled liquid branch (L) and two glass branches (G1 and G2) ; the latter are characterized by a non-vanishing structural order parameter. Explicit calculations of the free énergies of the three branches as functions of volume, for fixed T, point to the existence of a first-order phase transition between the L and G2 branches, characterized by very weak discontinuities of the volume and entropy of the coexisting phases. The transition occurs at a temperature above the Kauzmann temperature TK (where the configurational entropy vanishes), so that the « Kauzmann catastrophe » is preempted by the RFOT.
