Stokes-Einstein relations for a square-well fluid.

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Soft Matter Physics

Background:

• The Stokes-Einstein relation connects shear viscosity (eta) and self-diffusion (D) in fluids.
• Understanding deviations from this relation is crucial for complex fluids.

Purpose of the Study:

• To construct and analyze a Stokes-Einstein relation for a classical fluid with square-well potentials.
• To investigate the contributions of multi-body interactions to viscosity and diffusion.

Main Methods:

• Utilized a Smoluchowski equation for pair diffusion dynamics.
• Separated time correlation functions for eta and D into contributions from hard-sphere and square-well forces.
• Analyzed two-, three-, and four-body correlation functions.

Main Results:

• Self-diffusion (D) exhibits activated, Arrhenius-like behavior.
• The product of D and eta adheres to the Stokes-Einstein relation at the two-body level, with minor corrections for soft potentials.
• Three-body correlations enhance D, while higher-order correlations in eta partially offset each other.
• Deviations from the Stokes-Einstein law are primarily attributed to three-body correlation functions in D.

Conclusions:

• The study provides a detailed molecular-level analysis of the Stokes-Einstein relation in a model fluid.
• Three-body interactions are identified as the key source of deviation from the Stokes-Einstein law, particularly influencing self-diffusion.