GLASS FORMATION

The single most important outstanding issue in the field of glass formation is whether there is a length scale associated with dynamic heterogeneities and how it depends on temperature.  There are numerous models that have been proposed to interpret the underlying physics of the glass transition, but few effectively address the changing length scale associated with a super-cooled liquid.  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.


Figure 1 - Temperature dependence of the cooperative size, plotted in the form expected by dynamic scaling.  TC was calculated from data, where as the symbols represent cooperative size measured by DSC (open diamonds), 4-D NMR (closed diamonds), and diffusive experiments with tetracene (circles) and rubrene (triangles).  The solid line is the slope predicted by dynamic scaling.

Dynamic Scaling 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.  At sufficiently high temperatures the model ceases to apply to the relaxation times, and the crossover to a high-T Arrhenius temperature dependence provides an experimental estimate of the caging temperature, TA.


Figure 2 - Arrhenius plot of the temperature dependence relaxation times of PVAc from dielectric data [Richert2000, Stickel1995] (circles). The solid line is an Arrhenius fit to the high temperature relaxation times and the dotted curve is a fit from dynamic scaling to the low temperature relaxation times. The critical temperature is shown as the dashed line.

In the glassy state, the length scale for cooperative motion can become temperature-independent, so the model predicts relaxation times to have an Arrhenius temperature dependence.  As expected by the model, the same activation energy is observed both above and below the glass transition.


Figure 3 - Arrhenius plot of the temperature dependence of viscosity for TNB [Plazek1968]. The solid line is an Arrhenius fit to the high temperature viscosity data with activation energy Ehigh = 33 kJ/mole. The dashed curve is a fit of dynamic scaling to the near-Tg viscosity data with TC = 310K and Elow = 194kJ/mole. The dotted line is the Arrhenius prediction of the dynamic scaling model at temperatures far enough below Tg that x is independent of temperature, without the use of any adjustable parameters.

This material is based upon work supported by the National Science Foundation under Grant DMR-9977928 and DMR-0422079.

Any opinions, findings and conclusions expressed in this material are solely those of the authors and do not necessarily reflect the views of the National Science Foundation.
 

PUBLICATIONS

  1. R.H. Colby "Dynamic Scaling Approach to Glass Formation", Phys. Rev. E, 61, 1783 (2000).
     
  2. S. Kamath, R.H. Colby, S.K. Kumar, J. Baschnagel "Thermodynamic Signature of the Onset of Caged Dynamics in Glass-Forming Liquids", J. Chem. Phys., 116, 865 (2002).
     
  3. B.M. Erwin and R.H. Colby "Temperature Dependences of Relaxation Times and the Length Scale of Cooperative Motion for Glass-Forming Liquids", J. Non-Cryst. Solids, 307-310, 225 (2002).