A heterogeneous picture of α relaxation for fragile supercooled liquids

Abstract

We examine some of the consequences, and their connection to experiments on supercooled liquids, of a scaling model of heterogeneous relaxation that is based on the theory of frustration-limited domains. In particular, we focus on what appears to be the two slowest components of structural relaxation, the one usually described by a stretched exponential or a Cole–Davidson function and the somewhat faster, apparently power-law decay known as von-Schweidler relaxation. Based on our model we study the α-relaxation activation free energy, the imaginary part of the dielectric frequency-dependent susceptibility, the susceptibility-mastercurve of Dixon et al. [Phys. Rev. Lett. 65, 1108 (1990)], and the breakdown of the Stokes–Einstein relation for translational diffusion at low temperatures. We also obtain estimates for the characteristic domain sizes as a function of temperature. As with all mesoscopic approaches, a number of assumptions must be introduced, but they all fit the overall scaling picture that motivates this approach. The good agreement with experimental dielectric relaxation data on two representative supercooled liquids, salol and glycerol, though necessarily dependent upon adjustable parameters, gives support to the theory.