Simple picture of supercooled liquid dynamics: Dynamic scaling and phenomenology based on clusters

Although it is now well established that in glassy liquids, slow structural relaxation accompanies a correlated structural rearrangement, the role of such a correlation in the transport anomaly, and thus in the slow dynamics, remains unclear. In this paper, we argue from a hydrodynamic viewpoint that a correlated structure (cluster) with a characteristic size xi sustains the long-lived stress and dynamically couples with the hydrodynamic fluctuations; therefore, the dynamics of this cluster is the origin of themesoscopic nature of anomalous hydrodynamic transport. Based on this argument, we derive a dynamic scaling law for tau(alpha) (or eta, where eta is the macroscopic shear viscosity) as a function of xi : tau(alpha) (proportional to(eta)) proportional to xi(4). We provide a simple explanation for basic features of anomalous transport, such as the breakdown of the Stokes-Einstein relation and the length-scale-dependent decoupling between viscosity and diffusion. The present study further suggests a different physical picture: Through the coarse graining of smaller-scale fluctuations (less than or similar to xi), the supercooled liquid dynamics can be regarded as the dynamics of normal (cluster) liquids composed of units with a typical size of xi. Although the correlation length of hydrodynamic transport xi and the dynamic heterogeneity size xi(DH), which is determined by the usual four-point correlation function, reflect some aspects of the cooperative effects, the correspondence between xi and xi(DH) is not one to one. We highlight the possibility that xi(DH) overestimates the actual collective transport range at a low degree of supercooling.