Growth of the Cooperative Length Scale Below the Caging Temperature of Glass-forming Liquids

A cooperative mechanism is invoked to explain the acute property changes observed in glass-forming liquids near the glass transition temperature $T_g$. This theory implies the existence of cooperatively rearranging regions (CRR) as characterized by a dynamic length scale $\xi$, which is present in both experiments and simulation. Armed with the temperature dependence of this length scale and the fractal dimension of the CRR (from simulations) a simple scaling model for glassy behavior can be constructed. This scaling model has been applied to measurements of viscosity, the $\alpha$-relaxation and probe dynamics to estimate the $\xi(T)$ for numerous glass forming liquids.