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 β value of a stretched exponential response function, φ(t)0ex0ex=0ex0exe^-(t/τKWW)^β, and the fragility of the liquid. The β value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.