The Stokes–Einstein–Sutherland Equation at the Nanoscale Revisited

• Published in: Small (Weinheim an der Bergstrasse, Germany) Vol. 20; no. 6; pp. e2304670 - n/a
• Main Authors: Baer, Andreas, Wawra, Simon E., Bielmeier, Kristina, Uttinger, Maximilian J., Smith, David M., Peukert, Wolfgang, Walter, Johannes, Smith, Ana‐Sunčana
• Format: Journal Article
• Language: English
• Published: Germany Wiley Subscription Services, Inc 01.02.2024
• Subjects: analytical ultracentrifugation; boundary condition; Boundary conditions; Buckminsterfullerene; Diffusion coefficient; Dilution; Green–Kubo formalism; molecular dynamics; Simulation; Solvents; Stokes–Einstein–Sutherland equation; Toluene; boundary condition; analytical ultracentrifugation; Green-Kubo formalism; Stokes-Einstein-Sutherland equation; molecular dynamics
• ISSN: 1613-6810; 1613-6829; 1613-6829
• DOI: 10.1002/smll.202304670

The Stokes–Einstein–Sutherland (SES) equation is at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature, and the boundary condition for the particle‐solvent interface. It is assumed that it relies on the separation of scales between the particle and the solvent, hence it is expected to break down for diffusive transport on the molecular scale. This assumption is however challenged by a number of experimental studies showing a remarkably small, if any, violation, while simulations systematically report the opposite. To understand these discrepancies, analytical ultracentrifugation experiments are combined with molecular simulations, both performed at unprecedented accuracies, to study the transport of buckminsterfullerene C60 in toluene at infinite dilution. This system is demonstrated to clearly violate the conditions of slow momentum relaxation. Yet, through a linear response to a constant force, the SES equation can be recovered in the long time limit with no more than 4% uncertainty both in experiments and in simulations. This nonetheless requires partial slip on the particle interface, extracted consistently from all the data. These results, thus, resolve a long‐standing discussion on the validity and limits of the SES equation at the molecular scale. The Stokes–Einstein–Sutherland equation relates a particle's diffusion coefficient to its size. Statistical physics postulated the break down for particles comparable in size to the surrounding fluid molecules. Retrieving Stokes' friction coefficient in proper non‐equilibrium conditions, both experiments and simulations are shown to reproduce the correct Stokes–Einstein–Sutherland equation when relaxing the stick boundary conditions at the particle‐solvent interface.