Temperature dependence of the length scale for cooperative motion in glass-forming liquids

When considered in the framework of a dynamic scaling model, the length scale of cooperative motion of all glass-forming liquids appears to have a universal temperature dependence. This model also predicts relaxation times with a system specific temperature dependence, as the product of the universal cooperative length scale raised to the sixth power and a non-universal thermally activated process. This model was successfully applied to over 49 glass-forming liquids, including 14 novel indane-based glasses.; Rotational dynamics and translational diffusion of small anisotropic molecular probes are used to estimate the length scale of cooperative motion in a model-independent manner for five glass-formers. This length scale agrees quantitatively with the length scale obtained in 4-D NMR experiments which is known to measure the size of the slow relaxing regions. Temperature dependence of self-diffusion, dielectric alpha-relaxation time and viscosity each provide model-dependent length scales that are proportional to the cooperative length scale utilized by the dynamic scaling model. Each of these methods are self consistent and collectively prove that the cooperative length grows as temperature is lowered below the "caging" temperature TA, below which dynamics are cooperative in nature. This length appears to diverge at a temperature 10-20 K below the glass transition temperature T g for fragile glass-formers.; Employing the tested framework of dynamic scaling, the cooperative lengths at Tg and TA are estimated for three molecular glass-formers and three polymeric glass-formers. At TA, the cooperative length for molecular glass-formers is found to be approximately the van der Waals radius of the molecule. Assuming this result to be general, the cooperative length at Tg for fifteen other glass-forming liquids is estimated, resulting in the conclusion that 2 nm ≤ xi(Tg) ≤ 10 nm.