Critical Scaling in Glassy Glasses

Abstract

In the spirit of a description which is due to Angell¹ figure one contrasts two different behaviours of glass-forming liquids: the viscosity of the “strong” systems follows an Arrhenius law and they exhibit a small specific heat anomaly. The viscosity of the “fragile” systems, by contrast, is better described by a Fulcher law η = η_o exp(-B(T-T_F)) and there is a large specific heat anomaly above T_F a temperature where it seems that the viscosity would diverge and, at the same time, that the total excess entropy S of the liquid phase would cancel in the glassy state : Kauzmann paradox². The Adam and Gibbs theory³, precisely, relates the viscosity variation to an activation over a poten ial barrier which diverges when the entropy S cancels: η/η_o ~ τ/τ_o ~ exp(C/(TS)). The entropic catastrophy therefore cannot occur in a finite time. In practice experiments at equilibrium are restricted to temperatures larger than T_g, the “glass temperature”, where the viscosity reaches 10¹³ poises which would correspond to a relaxation time for shear deformation of the order of τ ~ G_∞η ~ 10⁴ s (i.e. about the longest times which we are ready to wait).