Microscopic Theory of Heterogeneity and Nonexponential Relaxations in Supercooled Liquids

Recent experiments show that supercooled liquids around the glass transition temperature are “dynamically heterogeneous” [H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999)]. Such heterogeneity is expected from the random first order transition theory of the glass transition. Using a microscopic approach based on this theory, we derive a relation between the departure from Debye relaxation as characterized by the $\beta$ value of a stretched exponential response function, $\phi \left(t\right){=e}^{-(t/{\tau }_{\mathrm{KWW}}{)}^{\beta }}$, and the fragility of the liquid. The $\beta$ value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.