Tuesday, August 5, 2014

Stokes-Einstein relation between viscosity and diffusion in liquids

The Stokes-Einstein equation
relates the diffusion constant D of a macroscopic particle of radius r undergoing a Brownian motion to the viscosity eta of the fluid in which it is immersed.
It is a beautiful and simple example of a fluctuation-dissipation relation.

But suppose now we think about one of the individual atoms or molecules in the fluid. It also undergoes Brownian motion and one can define a self-diffusion constant.
It is amazing to me that the Stokes-Einstein relation still holds for a wide range of liquids, temperatures, and pressures with r being of the order of the molecular radius.

The figure and table below are taken from this paper.

Can this relation be derived from microscopic theory?
Zwanzig gave a heuristic justification here.
Rah and Eu gave a derivation from stat. mech. here.

The Stokes-Einstein relation does break down as one approaches the glass temperature in a supercooled liquid, as for example shown here. The origin of that breakdown is controversial, as is many phenomena involving glasses.

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