Stokes–Einstein Relation
The Stokes–Einstein (or Stokes–Einstein–Sutherland, SES) relation connects the self-diffusion coefficient D of particles in a liquid to the liquid’s shear viscosity η through d = kB T/(2πηD), where d is an effective hydrodynamic diameter. It follows from combining the Einstein relation for Brownian motion with Stokes drag on a sphere, so it assumes independent, randomly moving, roughly spherical particles. In many liquids d is nearly constant over a temperature range, which lets one property be estimated from the other. A common generalization is the fractional Stokes–Einstein form D/T ∝ η(-κ), where κ = 1 recovers the SES and smaller exponents (often 0.6 to 1) signal a breakdown. Deviations typically appear in supercooled or near-melting liquids, and their origin (local structure, dynamic heterogeneity, species decoupling) is debated. Computing D and η from simulation is covered under transport properties from molecular dynamics, and one structural explanation is icosahedral order.
Deviation in liquid Al–Si from icosahedral clusters (2022)
Zhan and Kitchin used classical molecular dynamics of Al0.90Si0.10 and Al0.94Si0.06 to show that the effective diameter is constant from about 1400 K to the melting point (630 K and 700 K in their model) and deviates below it, with a fitted κ of 0.97 ± 0.01. Per-atom transport estimates showed that icosahedral clusters raise the viscosity but leave diffusion unchanged, and excluding cluster atoms restored κ to 1.00 ± 0.02 and 0.99 ± 0.02, identifying the clusters as the origin of the deviation (Zhan 2021). Summary: zhan2022b.