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.

Comparing Microscopic and Macroscopic Dynamics in a Paradigmatic Model of Glass-Forming Molecular Liquid

“…Intriguingly, the crossover between the two regimes does not affect the temperature-dependence of the average square jump length . Similarly, we find that a fully microscopic relation among CJ time and length scales, , recently reported for other glass-formers [ 38 ], holds in good approximation throughout the investigated temperature range.…”

“…Thus, the decoupling of and is not only a proxy of macroscopic SEB, as suggested elsewhere [ 27 , 28 , 29 , 38 , 48 , 49 , 50 , 51 ], but also a precursor of this phenomenon, being already clearly detectable just below the crossover temperature.…”

“…Interestingly, such crossover temperature also coincides with the onset of deviations from MCT-like behaviour. We find that, at variance with other systems, in which the two ratios and are linearly related on decreasing temperature [ 38 ], in the present case the microscopic ratio actually increases quite faster than the macroscopic one when the low-temperature regime is entered. Hence, the decoupling of the CJ timescales and in 3d KALJ liquid not only is a proxy of the macroscopic SEB, but can also be seen as an “early-warning” (in temperature) of its occurrence.…”

“…Finally, we find a linear relation between and , which suggests the existence of a correlation between the fundamental length and time scales of CJ motion. Noticeably, this feature appears also in other glass-forming liquids [ 38 ]. It is interesting to underline that this fully microscopic relation seems to be unaffected by the crossover between the the two temperature regimes.…”

“…Finally, in Figure 5 , we test an interesting result, recently obtained for different glass-forming liquids [ 38 ], namely, the linear relation , providing a connection among the three CJ microscopic quantities. We do find that this fully microscopic relation works very well also for the 3d KALJ liquid investigated here.…”