Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective

Abstract

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τατD between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τατD∝⟨tp⟩⟨tc⟩, where ⟨tp»and ⟨tc»are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τα∝⟨tp⟩⟨ΔrJ2⟩ and τD∝⟨tc⟩⟨ΔrJ2⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨ΔrJ2⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.