Bridging the gap between the mode coupling and the random first order transition theories of structural relaxation in liquids

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating, in a self-consistent way, the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated hopping events called instantons. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event. In the vertex, the probability is proportional to exp(-A/s(c)) where s(c) is the configurational entropy. Close to the glass transition temperature, T-g, since s(c) is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor, phi(t), in deeply supercooled liquid fairly well. We show that below the mode coupling transition temperature, T-c, phi(t) not only decays via the hopping channel but the otherwise frozen MCT part of phi(t) also shows a hopping induced decay. This decay is primarily due to the relaxation of the longitudinal viscosity which is otherwise divergent in the idealized MCT. We further show that although hopping motion induces a decay in the MCT part of phi(t), due to the self-consistent calculation, this effect is nonlinear in nature.