Stokes radius

The Stokes radius, Stokes-Einstein radius, or hydrodynamic radius R_H, named after George Gabriel Stokes, is not the effective radius of a hydrated molecule in solution as often mentioned. Rather it is the radius of a hard sphere that diffuses at the same rate as the molecule. The behavior of this sphere includes hydration and shape effects. Since most molecules are not perfectly spherical, the Stokes radius is smaller than the effective radius (or the rotational radius). A more extended molecule will have a larger Stokes' radius compared to a more compact molecule of the same molecular weight.

In liquids where there are considerable interactions between solute and solvent molecule, the Stokes' radius (of a perfect sphere) is proportional to frictional coefficient f and inverse proportional to viscosity η as follows:

$\ R_H=\frac{k_BT}{6\pi \eta D}.$

where, k_B is the Boltzmann constant (in J K⁻¹), D is the diffusion coefficient (in m²s⁻¹) and T is the temperature in kelvins. The frictional coefficient is determined by the size and shape of the molecule under consideration.

See also

• Capillary electrophoresis
• Hydrodynamic radius
• Dynamic light scattering
• Stokes' law
• Equivalent spherical diameter