The glass transition: dynamic and static scaling approach

We discuss the viscosity and the specific heat of glass forming systems near their glass transition in the framework of usual scaling theory at a second order transition. We define this transition through the Kauzmann paradox : i.e. we assume that all the entropy difference between the same crystal and the liquid phase is found over the critical temperature Tc where the viscosity also would diverge as a manifestation of critical slowing down. We provide expressions for different « dimensionalities » between the lower critical and higher critical dimensions which would be appropriate to describe all situations between the « fragile » and the « strong » cases. In practice it seems that each system undergoes a cross-over (or a high order liquid to liquid transition) from fragile to strong behaviour when the viscosity is of the order of a thousand poises.