The Stokes-Einstein-Sutherland Equation at the Nanoscale Revisited

Area of Science:

• Statistical Physics
• Physical Chemistry
• Molecular Dynamics

Background:

• The Stokes-Einstein-Sutherland (SES) equation is a cornerstone of statistical physics, linking particle diffusion to fluid properties.
• Its applicability at the molecular scale is debated due to scale separation assumptions, with experimental and simulation results often conflicting.
• Understanding these discrepancies is crucial for accurately modeling nanoscale transport phenomena.

Purpose of the Study:

• To investigate the validity of the Stokes-Einstein-Sutherland equation at the molecular scale.
• To reconcile conflicting experimental and simulation data regarding the SES equation's limitations.
• To determine the transport behavior of buckminsterfullerene (C60) in toluene at infinite dilution.

Main Methods:

• Combined analytical ultracentrifugation experiments and molecular simulations at high accuracy.
• Studied the transport of buckminsterfullerene (C60) in toluene at infinite dilution.
• Analyzed data using linear response theory to a constant force.

Main Results:

• The studied system (C60 in toluene) violates the slow momentum relaxation conditions required by the SES equation.
• Despite violations, the SES equation is recovered in the long-time limit with less than 4% uncertainty in both experiments and simulations.
• Partial slip at the particle interface was consistently identified as a key factor.

Conclusions:

• The Stokes-Einstein-Sutherland equation remains valid at the molecular scale, even under conditions violating its traditional assumptions.
• Partial slip at the particle-solvent interface is essential for reconciling experimental and simulation data and validating the SES equation.
• This study resolves a long-standing debate on the limits of the SES equation in molecular transport.