Possible universal relation between short time β-relaxation and long time α-relaxation in glass-forming liquids

Relaxation processes in supercooled liquids are known to exhibit interesting complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is the occurrence of multiple steps of relaxations. The shorter time relaxation is known as the β-relaxation which is believed to be due to the motion of particles in the cage formed by their neighbors. The longer time relaxation is called the α-relaxation. The time scales of these two relaxations processes dramatically separate out with supercooling. In spite of decades of research, it is still not clearly known how these relaxation processes are related to each other. In this work, we show that there is a possible universal relation between short time β-relaxation and long time α-relaxation. We also show that the proposed relation can be rationalized within random first order transition theory of glass transition if power law relation is assumed between static and dynamic length scales.