Understanding the Stokes–Einstein relation in supercooled liquids using random pinning

Abstract

The breakdown of the Stokes–Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomenon has been studied in depth over many years in efforts to understand the microscopic mechanism, without much success. Recently it was found that the violation of the Stokes–Einstein relation in supercooled liquids can be tuned by randomly pinning a set of particles in their equilibrium positions. This observation suggested a possible framework where the breakdown of the Stokes–Einstein relation in the dynamics of supercooled liquids can be studied in a systematic manner. We have performed extensive molecular dynamics simulations to understand this phenomenon by analysing the structure of appropriately defined sets of dynamically slow and fast particle clusters. The breakdown of the Stokes–Einstein relation is found to become predominant once the cluster formed by the slow particles percolates the entire system size. Finally we propose a possible close connection between fractal dimensions of these clusters and the exponents associated with the fractional Stokes–Einstein relation.