Temperature dependence of intermediate-range orders in the viscosity-temperature relationship of supercooled liquids and glasses.

The viscosity-temperature relationship obtained by us for several glasses over a wide temperature range was analyzed by extending the Adam-Gibbs theory to the range below the glass transition temperature (T(g)). The entropy change of the intermediate-range orders (IROs) is discussed on the basis of the theory developed by Prigogine. It is estimated that the time dependence of the vibrational entropy of a glass shows a constant decrease with a smallest change, while that of its configurational entropy is 0, keeping the constant fictive temperature and the isostructural state. The result predicts the decrease of the volume of a glass at the constant time-rate through spontaneous aging at the constant temperature. We also show that the glass transition is a phase transition from an equilibrium Vogel-Fulcher-Tamman state to a nonequilibrium and (meta-)stable Arrhenius state through fluctuations at T(g), and a microscopic feature of the glass transition is the self-organization of the IROs. These findings are extremely useful in analyzing glass and nanomaterial productions because the size of the IROs in the glass state is a few nanometers.