Emergence of cooperatively reorganizing cluster and super-Arrhenius dynamics of fragile supercooled liquids

In this paper, we develop a theory to calculate the structural relaxation time tau(alpha) of fragile supercooled liquids. Using the information of the configurational entropy and structure, we calculate the number of dynamically free, metastable, and stable neighbors around a central particle. In supercooled liquids, the cooperatively reorganizing clusters (CRCs) in which the stable neighbors form "stable" nonchemical bonds with the central particle emerge. For an event of relaxation to take place, these bonds have to reorganize irreversibly; the energy involved in the processes is the effective activation energy of relaxation. The theory brings forth a temperature T-a and a temperature-dependent parameter psi(T) which characterize slowing down of dynamics on cooling. It is shown that the value of psi(T) is equal to 1 for T > T-a, indicating that the underlying microscopic mechanism of relaxation is dominated by the entropy-driven processes, while for T < T-a, psi(T ) decreases on cooling, indicating the emergence of the energy-driven processes. This crossover of psi(T) from high to low temperatures explains the crossover seen in tau(alpha). The dynamics of systems that may have similar static structure but very different dynamics can be understood in terms of psi(T). We present results for the Kob-Anderson model for three densities and show that the calculated values of tau(alpha) are in excellent agreement with simulation values for all densities. We also show that when psi(T), tau(alpha), and other quantities are plotted as a function of T/T-a, (or Ta/T), the data collapse on master curves.