Speculations on the Glass Trans

I speculate about the ingredients needed for a theory of the liquid+glass transition. Experimental phenomenology suggests that there is an underlying equilibrium thermodynamic transition. Because of a breakdown of hyperscaling, the free-energy barriers to relaxation diverge at the critical point leading to a Vogel-Fulcher-like divergence of the characteristic relaxation times. The glass is thus a material trapped just above its critical point. Why(') are glasses solid? From a chemist's point of view, the answer is simple: glasses are bonded together into a rigid network. From a physicist's point of view, rigidity is much more subtle. If a glass is solid, then it must be separated by a phase transition from the liquid state; the transition occurs when the viscosity first becomes infinite. The experimental answer is that glasses are not solid. As one cools from the liquid state [2] the viscosity does rise sharply in a narrow temperature range, but below this .glass transition. the viscosity continues to rise, with an apparent Arrhenius law (fig. 1). However, at low temperature Arrhenius behavior is due to the failure of the material to stay in equilibrium. As one cools more slowly, the viscosity rises to higher values before crossing over, and rises with a steeper slope afterward (2) (fig. 1). Thus it is reasonable to postulate an underlying equilibrium phase transition into a truly solid state, which drives the material from liquid to glassy behavior. Perversely, it is because the viscosity grows so quickly that it is hard to study whether and how it diverges(3). However, a wide variety of liquids, when (l) This paper is intended to review well-known phenomena related to the glass transition, in order to advocate a general approach to the problem. I make no claims that this is a theory: no new insights into the nature of the order parameter are presented here. At places the text will be inescapably vague. (The alternative of making up a detailed model was explored in the free-volume theories [ll, which at least show that such models are possible.) To avoid an endless series of caveats, I w i l l write as if my position were established as the correct one: references to critical phenomena will be made as if an underlying second-order phase transition were known to exist. (2) This is why many people say that glass fkeezing is a *dynamical transition*. However apt this phrase may be, it …