Friction Coefficients and Molecular Parameters

This expression is known as the Stokes-Einstein equation. This formula correctly relates diffusivity to molecular dimensions and viscosity for cases in which Stokes law is applicable. 

Stokes law—although strictly valid only for spheres—yields a good approximation for the dependence of f on the size of small particles and molecules. However, a few modifications and limitations must be noted. First, as stated above, Stokes law was derived for macroscopic spheres in motion in a continuous medium, not for molecular sized bodies moving 

Molecules, of course, are generally no closer to ellipsoids than to spheres. Nonetheless, the results of Perrin clearly show the order of magnitude of the effects of molecular elongation and flattening—and by implication the effects of other geometric distortions as well. 

In that molecules of similar geometries have / values proportional to some linear dimensions (such as maximum length or radius), we find that /is related to molecular weight M by the approximate expression 

However, for linear polymers existing as random coils in solution, f increases in rough proportion to M1/2. 

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