On the nature of supercooled and glassy states of matter

The temperature dependence of relaxation behavior in glass-forming liquids is formulated in terms of the temperature variations of a critical lower limit z∗ to the sizes of cooperative regions that can rearrange into another configuration independent of its environment. The temperature dependence of the size of this cooperatively rearranging region is determined by dividing the total volume of the system into blocks, each of volume L3, and then relating the number of particles or molecular segments in each block to the entropy per block, to the Gibbs free energy per block, to the molar entropy of the macroscopic sample, and to the temperature derivative of block length L. The result of the molecular-kinetic theory is a relation for the relaxation time which almost coincides with the empirical WLF and VTF equations. The theory is applied to viscosimetric experiments. This permits evaluation of the ratio of the kinetic glass temperature Tg to the equilibrium temperature T2, where the size of the rearranging region diverges. Predictions are made concerning the temperature dependence of relaxation times and the activation energy for viscous flow as T→Tg, and the ratio of the enthalpy of the glass to the enthalpy of supercooled liquid. The values of Tg/T2 obtained for fourteen widely different materials were found to be nearly the same, i.e., 1.28 ± 5.78%. The non-linearity of the glassy state is found to be governed by properties of the equilibrium melt above Tg. Finally, for an arbitrary one-component many-body system we obtain a lower bound to the entropy density at low temperatures. The entropy per unit volume is related to integrals over certain temperature-dependent correlation functions of the system. An operator product expansion of the correlation functions leads to a necessary condition for the existence of the Kauzmann temperature.