Origin of the difference in the temperature dependences of diffusion and structural relaxation in a supercooled liquid
In this paper we address the relationship between vari ous time scales of a liquid as it approaches the glassy state. The comparison of the self-diffusion constant DT and shear viscosity η is probably the most studied of these relationships . Well above any glass transition, the scaling Dj ĩ ) /T = const (the Stokes-Einstein relation) holds for a wide range of liquids, supporting the assump tion that particle friction at these temperatures arises from the viscous dissipation of the associated velocity field in the surrounding liquid. Recently, a number of studies [2 ,3] on a range of organic glass formers have shown that this relation breaks down as the supercooling is increased, with Dt proving to be larger than expected. The rota tional diffusion constant Dr , however, continues to scale with η well below the temperature at which the scaling breaks down for Dj,
The most popular explanation of this difference in the temperature dependences of these two time scales (either
and η , or DT and D r ) invokes the existence of a spatially heterogeneous and transient distribution of lo cal relaxation times [1,2,4-6]. The mean-squared par ticle displacement (MSD) and the relaxation of the stress correlation function corresponds to different averages over this distribution. The former average is dominated by the more mobile particles, while the stress correlation func tion is dominated by the slower regions. As the dis tribution broadens (and becomes more asymmetric) on cooling, so does the difference between the different av erages increase. The proposal makes sense, particularly as the existence of the dynamic heterogeneities have been established experimentally (as long-lived kinetic subpopu lations ) and from computer simulations (as spatially re solved domains [8,9]). This proposal, however, has yet to be directly tested.