On the glass transition singularities and slow dynamics

We give a unified view for the glass transition singularities and slow relaxations in supercooled liquids. On the basis of a heuristic argument, we show that the waiting time distribution (WTD) function for the non-trapped diffusive motion is given by a power-law function in the long time limit. Exploiting the lattice model for the stochastic dynamics, we show that the divergence of various moments of the WTD signifies dynamical anomalies which can be assigned to the Vogel-Fulcher (TVF), glass transition (Tg) and crossover (Tx) temperatures in supercooled liquids. Three predictions (i) the Kauzmann temperature TK = TVF, (ii) TgSC(Tg) ∼ constant and (iii) TxSC(Tx)/TgSC(Tg) = 2, where SC(T) is the excess entropy per atom, are made which are consistent with experimental observations.