The role of cluster dynamics in the α-relaxation of supercooled liquids

The effect is considered of molecules leaving a cluster, within which their dielectric α-relaxation is described by a stretched exponential function p(t) = exp[-(t/τ₀)^α]. It is shown that an increase in their rate of leaving can lead to the relaxation of the system's polarization being described by a stretched exponential function with a stretching exponent larger than α and a relaxation time smaller than τ₀. The implications of this for time-temperature superposition and other properties of supercooled liquids are discussed.